Linear Programming Questions and Answers

92 XY that is the intersection of the plane seen from above Evaluate any integrals by hand giving an exact answer Be sure to include all of your work for this problem No work means no credit a Draw a graph of the given region and include it with your written work b Convert the following line integral using Stokes Theorem into an integral over the region bounded by C using polar coordinates and then compute its value 7 d nted counter clockwis dr de

A zookeeper has a walrus with a nutritional defici of vitamin B 1 and 1500 mg of vitamin B 2 One vitamin B 2 and costs 0 07 One Healthovite pi costs 0 05 Complete parts fal c bolow

A study of about 1 800 U S colleges and universities resulted in the demand equation q 9 600 2 4p where q is the enrollment at a college or university and p is the average annual tuition plus fees it charges a The study also found that the average tuition charged by universities and colleges was 3 000 What is the corresponding price elasticity of demand Round your answers to two decimal places Is the price elastic or inelastic O elastic inelastic Should colleges charge more or less on average to maximize revenue O more less b Based on the study what would you advise a college to charge its students in order to maximize total revenue per student What would the revenue be

X 3X 4 8 Find the minimum and maximum if they exist of the objective function f subject to the constraints Objective function f 7x 6y 7x 5y 2100 Constraints 2x 5y 2 50 x 20 y 20

Use this for questions 21 22 Yawaka manufactures motorcycles and bicycles To stay in business the number of bicycles made cannot exceed four times the number of motorcycles They lack the facilities to produce more than 90 motorcycles or more than 200 bicycles and the total production of motorcycles and bicycles cannot exceed 250 If Yawaka makes 1200 on each motorcycle and 370 on each bicycle how many of cach should be made to maximize profit They should make They should make motorcycles bicycles

ve the linear programming problem Maximize 2x 5y subject to x 2y 10 3x 2y 18 x20 y 0 ect one a 32 b 23 c 25

Solve the linear programming proble Maximize C 4x 3y subject to x 4y 32 2x y 10 x 0 y 0

The time required to play a certain board game is uniformly distributed between 15 and 60 minutes Use the formula U a b a x RAND for a uniform distribution between a and b to obtain a sample of 50 outcomes and compute the mean minimum maximum and standard deviation Click the icon to view the randomly generated times Determine the appropriate formula U 15 60 15 RAND Type whole numbers Fifty random values generated using the formula are now provided in the problem statement Compute the mean The mean is minute s Round to one decimal place as needed Randomly generated Times k 59 65875 18 94221 21 60876 49 26038 46 69202 D 52 89645 37 74858 25 84536 34 93642 59 59418 30 95933 56 47676 49 24393 30 11539 33 52403 55 78600 49 70706 24 98502 58 66661 19 55243 45 97866 39 08874 47 94008 16 38098 41 77787 18 78114 47 79485 36 93377 35 44829 25 97972 31 89785 32 38128 17 89216 49 06946 45 38556 27 25673 54 79284 25 82267 47 21793 43 70658 36 55512 35 85211 44 35708 56 88593 41 70251 44 61141 49 38174 30 53574 41 09028 31 45312 X

HISTOIR Part A Zookeeper has a walrus with a nutritional deficiency She wants One Maxivite pill contains 400 mg of iron 200 mg of vitamin B 1 150 mg of vitamin B 2 and costs 0 05 Complete parts a c b a What combination of Maxivite and Healthovite pills will meet t Set up the linear programming problem Let m represent the num

H The number of parking tickets issued in a certain city on any given weekday has a Poisson distribution with parameter 50 Round your answers to four decimal places a Calculate the approximate probability that between 35 and 80 tickets are given out on a particular day b Calculate the approximate probability that the total number of tickets given out during a 5 day week is between 215 and 275 c Use software to obtain the exact probabilities in a and b and compare to their approximations Calculate the exact probability that between 35 and 80 tickets are given out on a particular day Calculate the exact probability that the total number of tickets given out during a 5 day week is between 215 and 275

Suppose your waiting time for a bus in the morning uniformly distributed on 0 10 whereas waiting time in the evening is uniformly distributed on 0 16 independent of morning waiting time a If you take the bus each morning and evening for a week what is your total expected waiting time Assume a week includes only Monday through Friday Hint Define rv s X X10 and use a rule of expected value min b What is the variance of your total waiting time Round your answer to two decimal places min2 c What are the expected value and variance of the difference between morning and evening waiting times on a given day Use morning time evening time Round the variance to two decimal places expected value variance min min d What are the expected value and variance of the difference between total morning waiting time and total evening waiting time for a particular week Use morning time evening time Assume a week includes only Monday through Friday expected value min min variance

8 Find the minimum and maximum if they exist of the objective function f subject to the constraints Objective function f 7x 4y Constraints 5x y 60 x 6y 60 4x 6y 2 204 120 520

TIDE a Dam gates need to be put across a river Which type of dam gates will best stop an incoming tide b A C OB TIDE

Planning a Diet Paul s diet is to contain at least 24 units of carbohydrates and 16 units of protein Food substance A costs 1 40 per unit and each unit contains 3 units of carbohydrates and 4 units of protein Food substance B costs 0 90 per unit and each unit contains 2 units of carbohydrates and 1 unit of protein How many units of each food substance should be purchased in order to minimize cost What is the minimum cost int Define variables and write a system of inequalities to begin

Give a Big O estimate for 5x e 10x x 0 e OO x 3 0 x e 0 x 3

A company makes 2 types of computers X and Y The company can make a total of 80 computers per day and it has 240 work hours available per day It takes 2 work hours to make computer X and 6 hours to make computer Y The profits on computer X is 80 and the profit on computer Y is 120 How many of computer X and computer Y must be made to maximize profit Maximum Profit p at

Any point on the parabola can be labeled z y as shown 3 3 3 2 2 O Show Transcribed Text

Graph the exponential function g x 3 2 To do this plot two points on the graph of the function and also draw the asymptote Then click on the graph a function button Additionally give the domain and range of the function using interval notation 8 6 4 2 2 6 0 X Domain Range 0 0 0 0 0 0 8 X 8

0 2t The concentration in g ml of a drug t hours after being injected is given by C t t 10 the time when the concentration is at a maximum Give your answer accurate to at least 2 decimal places hours Find Find the maximum drug concentration Again give an answer accurate to at least 2 decimal places g ml

6 122 WP SS An electrically driven pump operating at steady state draws water from a pond at a pressure of 1 bar and a rate of 50 kg s and delivers the water at a pressure of 4 bar There is no sig nificant heat transfer with the surroundings and changes in kinetic and potential energy can be neglected The isentropic pump effi ciency is 75 Evaluating electricity at 8 5 cents per kWh estimate the hourly cost of running the pump

6 92 WP Water vapor at 5 bar 320 C enters a turbine operating at steady state with a volumetric flow rate of 0 65 m s and expands adiabatically to an exit state of 1 bar 160 C Kinetic and potential energy effects are negligible Determine for the turbine a the power developed in kW b the rate of entropy production in kW K and c the isentropic turbine efficiency

2 This is a continuation of the previous problem Recall that X X X7 be the number empty boxes when 10 distinct balls are randomly distributed into 7 distinct boxes In this question we are interested in finding the variance Var X of X a Show that X X X X XiX i 1 1si j 7 i j b Argue that E X E X for all 1 i 7 Hint Compare X and X c Show that for i j 510 E X X 710 d Finally using Var X E X2 E X to find Var X

162 The graph of y YA 4 3 2 1 0 t 1 2 3 2 e t dt where is a piecewise linear function is shown here 4 5 a Over which intervals is b Over which intervals is c What is the average value of l 6 X positive Over which intervals is it negative Over which if any is it zero increasing Over which is it decreasing Over which if any is it constant

Q2 Draw a sketch of the following function Make sure you include all the details such as the domain intervals of increase and decrease intervals of concavity maximum minimum inflection points x and intercepts and the asymptotes albeit if any of the above information is relevant and exists 6 Marks y 4x 2x 8 x 16

Find the minimum value of the function z 6x 3y subject to the following constraints x 16 y 13 9x 2y 62 x 5y226 Note that the ALEKS graphing calculator can be used to make computations easier N 08

Solve by the method indicated Express your answers in simplest radical form where appropriate Clearly state your solution set a 4x 12x 5 0 quadratic formula 4x 11x 3 0 factoring 1 c 2x 8x 5 0 complete the square b 3 4 5

Find the maximum value of the function z 7x 5y subject to the following constraints x 3 y 3 3x 4y 45 Note that the ALEKS graphing calculator can be used to make computations easier 0 010 ola

Find the maximum value of the function z 4x 5y subject to the following constraints 5x 1ly 88 x y 14 x 0 y20 Note that the ALEKS graphing calculator can be used to make computations easier 0

Yang s Material Company hauls gravel to a construction site using a small truck and a large truck The carrying capacity and operating cost per load are given in the accompanying table Yang must deliver a minimum of 420 cubic yards per day to satisfy her contract with the builder The union contract with her drivers requires that the total number of loads per day is a minimum of 8 How many loads should be made in each truck per day to minimize the total cost Small Truck Large Truck Capacity yd Cost per Load 60 66 70 59 In order to minimize the total cost the number of loads in a small truck that should be made is and the number of loads in a large truck that should be made is

tan B 2 Which of the following statements establishes the identity O A tan cot csc tan cos 1 2 sin 2 cot a csc 1 cos x 2 1 COS cot csc

Consider the simplex tableau given below X1 X2 X3 S1 S2 3 1 4 3 0 4 0 1 0 2 0 010 0 0 4 3 0 2 0 4 XX X3 S and z O X1 X2 X3 and x3 23223 1000N Which variables are nonbasic variables X3 3 and z X1 X3 and 1 X S and S X X and S 3339 23 23 28 19

ect choice below and if necessary fill in the answer box to complete your A

the number of flips to get the first HT Show that Y can be written as a sum of two independent 4 Suppose that we flip the coin with P H p E 0 1 until we get a pattern HT random variables and use this fact to find E Y

X1 2 0 4 3 20100 31000 S1 2 S3 0 0 4 4 2 4 2 1 0 X1 X3 S1 and z OX1 X2 X3 and x3 N MON3 TOOL Which variables are nonbasic variables 23 23 28 19

05 Section Quiz ength 2 00 00 2 3 Stephanie Vega Martinez Attempt 1 A company is building Laptops The model takes 3 hours to produce and model that takes 1 hour to produce have enough supplies to make 1000 and 1600 hours of labor Let x represent the number of delux and y represent the number of basi

Consider the function snippet below fun function x y 2 Z 0 FUNCTION BODY HIDDEN Which of the following corresponds to the same function call as fun 2 1 1 fun x 2 z 1 1 fun 1 2 1 fun 2 y y 1

Find the exact length of the arc intercepted by the given central angle in the figure to the right w 5 4x The length of the intercepted arc is Type an exact answer in terms of t Use integers or fractions for any numbers in the expression 10

and 20 4 equal to 4 or greater than 4 12 and 16 GCF is less than 4 DRAGAND DROP ITEMS 2 and 3 6 and 24 3 and 4 GCF is equal to 4 12 and 24 GCF is greater than DRAG AND DROP ITEMS

Find the Fourier series for g x 1 x pi x pi

Find the pivot in the simplex tableau EX X1 X2 X3 3 5 7 1 1 6 20 3 51 75 3

Find the pivot in the simplex tableau The pivot is located in row 0 0 column ACCE X1 X2 X3 1 24 4 4 1 1 0 3 3121 2 2111 2 1

The initial simplex tableau of a linear programmin L X1 X2 X3 S1 S2 R 13 17 315 2 1 0 NOO 0 0 13

A house is rented for 7 800 per quarter with each quarter s rent payable in advance If money is worth 6 compounded quarterly and the rent is deposited in an account what is the future valu the rent for one year Round your answer to the nearest cent x

Cullumber Company uses a periodic inventory system and reports the following for the month of June Date June 1 12 23 30 a1 Explanation Inventory Purchase Purchase Inventory a2 Units 120 eTextbook and Media Solution 390 Your Answer Correct Answer Used 190 Your answer is correct 235 Weighted average unit cost Cost of the ending Unit Cost Your answer is partially correct 5 Calculate weighted average unit cost Round answer to 3 decimal places e g 5 125 6 FIFO 7 Total Cost 600 1600 2 340 1 330 Compute the cost of the ending inventory and the cost of goods sold under FIFO LIFO and average cost Round answers to O decimal places e g 125 6 100 Attempts 3ATused LIFO Average cost 1433

186 Accounting The company s online sales rate s in dollars per hour followed a predictable daily pattern of elect one s t 100 25 cos 2 8 9 hours 8 7 hours 9 2 hours 8 6 hours 0 t 24 hours For how much of the day was the company s sales rate greater than 110 per hour Round to 1 d p GC

Large semitrailer trucks cost 75 000 each A trucking company buys such a truck and agrees to pay for it by a loan that will be amortized with 10 semiannual payments at 9 compounded semiannually Complete an amortization schedule for the first four payments of the loan Fill out the amortization schedule below Round to the nearest cent as needed Do not include the symbol in your answers Payment Amount of Payment Interest for Period Number Portion to Principal

Determine whether the given matrix is orthogonal 3 2 1 2 a 3 12 Q Q S O The matrix is orthogonal O The matrix is not orthogonal Find its inverse Enter sqrt n for n If it not orthogonal enter NA in any single blank

Solve the given initial value problem X 4 15 2 X X 0 46

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