Math - Others Questions

Prepare a master schedule given this information The forecast for each week of an eight week schedule is 60 units The MPS rule is to schedule production if the projected on hand inventory would be negative without it Customer orders committed are as follows Week Customer Orders 1 2 3 55 40 25 12 Use a production lot size of 90 units and no beginning inventory In the ATP row enter a value of 0 zero in any periods where ATP should not be calculated Leave no cells blank be certain to enter 0 wherever required June July Forecast Customer Orders Projected On Hand Inventory MPS 60 55 2 60 40 3 60 25 60 12 5 60 0 60 0 7 60 0 60 0

The forecast for each week of a four week schedule is 50 units The MPS rule is to schedule production if the projected on hand inventory would be negative without it Customer orders committed are follows Customer Order 52 35 Week 21234 538E 2582 20 12 Use a production lot size of 75 units and no beginning inventory Determine the available to promise ATP quantities for each period Leave no cells blank be certain to enter 0 wherever required

Wormwood Ltd produces a variety of furniture products The planning committee wants to prepare an aggregate plan for the next six months using the following information Demand Capacity Regular Overtime Regular time Overtime Cost Per Unit Period Subcontract Inventory holding per month MONTH 4 1 3 2 160 150 160 180 Forecast Output 150 10 Regular Overtime Subcontract Output Forecast Inventory 150 150 10 0 50 75 80 4 Click here for the Excel Data File Subcontracting can handle a maximum of 10 units per month Beginning inventory is zero Develop a plan that minimizes total cost No back orders are allowed Regular capacity Regular production Negative amounts should be indicated by a minus sign Leave no cells blank be certain to enter 0 wherever required 150 10 160 2 5 6 170 140 150 160 160 10 10 3 160 4 180 5 170 6 140 Total 960

1 Show that the inverse of an increasing function is increasing and the inverse of a decreasing function is decreasing 2 Find the functions f and g such that f g is even and f g is odd 3 f R a R b and f x is one to one and onto f x given What is the if x 1 x 3 if x 1 is given Find the value of a for the continuity of f x at x 1 4 f x 5 f x 2x a X x 4 is given Sketch the graph of f x 2x 11 3x 4 is

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A vehicle factory manufactures cars The unit cost C the cost in dollars to make each car depends on the number of cars made If x cars are made then the unit cost is given by the function C x 0 8x 256x 36 963 What is the minimum unit cost Do not round your answer

Systems 1 Create three different scenarios that can be modeled using linear systems 2 Solve each scenario using a different method graphing substitution elimination 18 100y no 29sed note 23001 st Yosmaye to exs add suley ismitge sob

For the real valued functions f x 5x 25 and g x x 2 find the composition fog and specify its domain using interval notation rea x 0 olo 5

The lease of Theme Park Inc is about to expire Management must decide whether to renew the lease for another 10 years or to relocate near the site of a proposed motel The town planning board is currently debating the merits of granting approval to the motel A consultant has estimated the net present value of Theme Park s two alternatives under each state of nature as shown below Suppose that the management of Theme Park Inc has decided that there is a 0 41 probability that the motel s application will be approved Options Renew Relocate Alternative a 1 If management uses maximum expected monetary value as the decision criterion calculate expected monetary value for the alternatives Renew and Relocate Renew Relocate Motel Approved 610 000 2 525 000 O Renew Motel Rejected 4 525 000 310 000 a 2 Which alternative should it choose Relocate Expected Value

hat range of P 1 would alternative A be the best choice if the goal is to maximize expected profit ose Alternative A if P 1 is less than 0 361 greater than 0 361 less than 25 greater than 25

A manager has compiled estimat nature The payoff table is as follows Alternative A B C Profit in thousands Click here for the Excel Data File profits for various capacity STATE OF NATURE 1 2 30 131 105 O Alternative A Alternative B O Alternative C O None 155 98 51 a Is there any alternative that would never be appropriate in terms of maximizing expected profit b For what range of P 2 would alternative A be the best choice if the goal is to maximize expected profit

The lease of Theme Park Inc is about to expire Management must decide whether to renew the lease for relocate near the site of a proposed motel The town planning board is currently debating the merits of granting approval to the mo A consultant has estimated the net present value of Theme Park s two alternatives under each state of nature as shown below What course of action would you recommend using Options Renew Relocate Click here for the Excel Data File a Maximin O Renew O Relocate b Maximax Relocate Renew Motel Approved 500 000 5 000 000 c Laplace Relocate Renew Motel Rejected 4 000 000 100 000

A manager must decide how many machines of a certain type to buy The machines will be used to manufacture a new gear for which there is increased demand The manager has narrowed the decision to two alternatives buy one machine or buy two If only one machine is purchased and demand is more than it can handle a second machine can be purchased at a later time However the cost per machine would be lower if the two machines were purchased at the same time The estimated probability of low demand is 30 and the estimated probability of high demand is 70 The net present value associated with the purchase of two machines initially is 75 000 if demand is low and 130 000 if demand is high The net present value for one machine and low demand is 90 000 If demand is high there are three options One option is to do nothing which would have a net present value of 90 000 A second option is to subcontract that would have a net present value of 110 000 The third option is to purchase a second machine This option would have a net present value of 100 000 How many machines should the manager purchase initially

The following diagram shows a 4 step process that begins with Operation 1 and ends with Operation 4 The rates shown in each box represent the effective capacity of that operation 12 hr Operation 1 Capacity 15 hr Operation 2 a Determine the capacity of this process per hour 11 hr Operation 3 14 hr Operation 4 b Which action would yield the greatest increase in process capacity 1 increase the capacity of Operation 1 by 15 percent 2 incroce the capacity of Operation 2 by 10 percent or 3 increase the capacity of Operation 3 by 10 percent

primary A producer of pottery is considering the addition of a new plant to absorb the backlog of demand that now exists being considered will have fixed costs of 7 400 per month and variable cost of 50 cents per unit produced Each item is sold to retailers at a price that averages 77 cents Round all answers to a whole number a What volume per month is required in order to break even Volume per month b What profit would be realized on a monthly volume of 51 000 units 67 000 units profits at volume of 51 000 profits at volume of 67 000 c What volume is needed to obtain a profit of 10 000 per month Volume d What volume is needed to provide a revenue of 30 000 per month

The following diagram shows a 4 step process that begins with Operation represent the effective capacity of that operation 11 hr 10 hr Operation 1 Operation 2 a Determine the capacity of this process Capacity per hour 12 hr Operation 3 18 hr Operation 4 b Which action would yield the greatest increase in process capacity 1 increase the capacity of Operation 1 by 12 percent 2 increase the capacity of Operation 2 by 14 percent or 3 increase the capacity of Operation 3 by 10 percent

A new machine will cost 24 000 but it will result in a savings of 4 000 per year What will the payback time be in years

A firm plans to begin production of a new small appliance The manager must decide whether to purchase the motors for the appliance from a vendor at 11 each or to produce them in house Either of two processes could be used for in house production Process A would have an annual fixed cost of 200 000 and a variable cost of 6 per unit and Process B would have an annual fixed cost of 165 000 and a variable cost of 7 per unit Determine the range of annual volume for which each of the alternatives would be best Round your first answer to the nearest whole number Include the indifference value itself in this answer For annual volumes of purchase from the vendor or less is best For annual volumes above that amount process A process B is best

1 Consider the three sets A the set of all even numbers B 2 4 6 C 2 3 4 6 a is set B a subset of set A b is set A a subset of set C c is set B a proper subset of set C write your answer in sentence form Yes No answer will not earn any credit 2 Consider the sets below Let U 1 2 3 10 A 1 3 5 7 B 1 2 3 4 C 3 4 6 7 9 1 Write the complement of set A use the proper set notation 2 Write the complement of set B use the proper set notation 3 Write AU B in set notation form 4 Write CnA in set notation 5 Write the set C

3 Consider the sets A red green blue B red yellow orange C red orange yellow green blue purple Find the following 1 Find A U B 2 Find An B 3 Find An C 4 Consider the sets A red green blue B red yellow orange C red orange yellow green blue purple Illustrate the VENN DIAGRAM for the following 1 Find A U B 2 Find An B find 45o

6 P x 2 x 7 write all the elements in set P 7 Q x 2 x 7 write all the elements in set Q 8 Is set P equivalence to set Q 9 R 1 2 3 4 5 6 and S 2 4 6 is set S a subset of set R 10 From question number 9 is set R a subset of set S 11 Write an example of a null or empty set 12 What is a proper subset and give an example of a proper subset

1 The set A 1 3 5 What is a larger set this might be a subset of 2 Given the set A a b c d List all of the subsets of A 3 From the given set A in number 2 what is the cardinality of set A 4 Given M set of days in the week what is the cardinality of set M 5 If set M set of days in the week and set S set of Snow White s dwarves is set M equivalence with set S why or why not

5 During March the business completed the following transactions Please use straight depreciation method for this case Please record the financial transactions and show adjusted trial balances 62 points a Borrowed 45 000 from the bank with Calderon signing a note payable in the name of the business 500 b Purchased supplies on credit 2300 Performed customer service and earned revenue on account 4 600 c d f i j Paid 200 on account Paid the following cash expenses salaries 5 000 rent 2 500 and interest Received 3 100 on account Received a 200 utility bill that will be paid next week Pruchased a computer workstation on credit 5000

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0 76 0 76 Determine the probability that the system will operate under each of these conditions a The system as shown Do not round your intermediate calculations Round your final answer to 4 decimal places Probability b Each system component has a backup with a probability of 76 and a switch that is 100 percent reliable Do not round your intermediate calculations Round your final answer to 4 decimal places Probability c Each system component has a backup with a probability of 76 and a switch that is 97 percent reliable Do not round your intermediate calculations Round your final answer to 4 decimal places

A product is composed of four parts In order for the product to function properly in a given situation each of the parts must function Two of the parts have a 0 88 probability of functioning and two have a probability of 0 74 What is the overall probability that the product will function properly Round your answer to 4 decimal places Probability

A system consists of 4 identical components In order for the system to perform as intended all of the components must perform Each has the same probability of performance If the system is to have a 0 82 probability of performing what is the minimum probability of performing needed by each of the individual components Round your answer to 4 decimal places

For the scenario given determine the smallest set of numbers for its possible values and classify the values as either discrete or continuous the number of presidents in U S history Choose the smallest set of numbers to represent the possible values integers irrational numbers natural numbers Orational numbers Oreal numbers whole numbers Are the values continuous or discrete O continuous

For the scenario given determine the smallest set of numbers for its possible values and classify the values as either discrete or continuos the fuel efficiency in miles per gallon for a fleet of rental cars Choose the smallest set of numbers to represent the possible values O integers O irrational numbers natural numbers Orational numbers Oreal numbers Owhole numbers Are the values continuous or discrete continu

For the scenario given determine the smallest set of numbers for its possible values and classify the values as either discrete or cont the number of rooms vacant in a hotel Choose the smallest set of numbers to represent the possible values O integers irrational numbers Onatural numbers Orational numbers Oreal numbers whole numbers Are the values continuous or discrete continuous

For the scenario given determine the smallest set of numbers for its possible values and classify the values as either discrete or c the number of presidents in U S history Choose the smallest set of numbers to represent the possible values O integers irrational numbers Onatural numbers Orational numbers Oreal numbers Owhole numbers Are the values continuous or discrete continuous

A group of numbers is given Choose the correct number line for the group of numbers being plotted the whole numbers less than 4 including 4 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1 0 1 2 4 5 6 7 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

Choose the correct number line for the number being plotted 10 30 4 3 2 1 1 2 3 4 5 6 3 2 1 0 1 2 3 4 5 6

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Write each polynomial in completely factored form One factor is given Find all the x intercepts zeros the y intercept then sketch the graph without a graphing calculato 1 f x x 9x 23x 15 x 5 2 f x x x 14x 24 x 3 94 SS

A group of numbers is given Choose the correct number line for the group of numbers being plotted the integers between 3 and 3 including 3 and 3 5 4 3 2 1 0 1 2 3 S 3 2 1 0 2 3 4 5 5 4 3 2 0 2 3 4 S

For the scenario given determine the smallest set of numbers for its possible values and classify the values as either discrete or continuous the number of stars a movie receives from critics where 1 star represents poor and 5 stars represents an epic Choose the smallest set of numbers to represent the possible values O integers irrational numbers natural numbers Orational numbers real numbers whole numbers Are the values continuous or discrete continuous Odiscrete

Determine the distance between the two given numbers Simplify your answer completely 18 and 2

Determine the distance between the two given numbers Simplify your answer completely 6 and 13

Choose the correct number line for the number being plotted 50 7 6 5 4 3 2 1 0 1 2 3 7 6 5 4 3 2 1 0 1 2 3

Choose the correct number line for the number being plotted 1 6 0 1 0 2 0 3 0 4 0 5 0 0 1 0 2 0 3 0 4 0 5

3 f x 5x 21x 21x 5 x 5 5x 641 4 f x 10x 37x 37x 6 5x 1 4

Consider the following group of numbers 6 4 8 3 14159265 0 6 7 17 List the integers Enter your answers as a comma separated list Round your answers to eight decimal places as neede

Consider the real number line shown here Determine whether the following number is between the two plotted values Yes 4 77 2 37 5 4 3 2 1 0 1 2 3 4 5 No 3 38

Rewrite the group of numbers ordered from least to greatest Enter your answers as a comma separated list 6 7 3 0 6 7

Choose the correct number line for the number being plotted 5 9 8 7 6 5 4 3 2 0 0 1 2 3 4 5 6 7 8 9

Alexis is making quarterly contributions of of 500 to her savings account which pays interest at the APR of 8 3 compounded quarterly Right after Alexis makes her 54th contribution the bank changes the APR to 9 and Alexis makes 36 more 500 contributions What is Alexis s balance right after her last contribution

Write the slope intercept form of the equation of each line given the slope and y intercept 11 Slope 1 y intercept 2 x 1x 2 13 Slope 3 y intercept 2 x 3x 2 1 15 Slope y intercept 1 2 Y X 1 17 Slope 7 y intercept 2 Y 7x 2 Sketch the graph of each line 19 y x 4 21 y 4x 5 10 5 3 4 3 5 4 3 2 1 0 A 3 2 12 Slope 13 y intercept 3 3x 3 32 14 Slope 4 16 Slope DIMIN 18 Slope y intercept 1 4 x 1 5 2X G y intercept 4 4 3 1 y intercept 0 20 y 5x 1 4 3 X 4 22 y x 5 4

You want to be able to withdraw 50 000 from your account each year for 30 years after you retire You expect to retire in 25 years If your account earns 10 interest how much will you need to deposit each year until retirement to achieve your retirement goals