Linear Programming Questions and Answers

Tutorial Exercise Set up the simplex matrix used to solve the linear programming problem Assume all variables are nonnegative Maximize f 9x 5y subject to 2x 7y 600 x 6y 375 Step 1 We want to set up the simplex matrix that would be used to maximize f 9x 5y subject to the following constraints 2x 7y 600 x 6y 375 We start by converting the constraint inequalities into equations by usin Select variables s and s This gives static 2x 7y S slack dynamic x 6y 600 375

rno runs a restaurant that sells two kinds of pies Arno knows the restaurant must make at least 9 and at nost 64 dozens of the Caramel Twists The restaurant must also make between 18 and 41 dozens of the Fluffy Deliciousness The dozens of Caramel Twists take 1 minutes in the oven while dozens of Fluffy Deliciousness equire 2 minutes in the oven The restaurant only has 108 minutes in the oven available If dozens of Caramel wists generate 1 76 in income and dozens of Fluffy Deliciousness generate 1 96 how many dozens of the ies should Arno have the restaurant make to get the most income Caramel Twists Fluffy Deliciousness

Solve for x Represent your answer on a number line x 4 6 Select one a b C d 3 3 3 2 2 2 0 0 2 3 2 3

Suppose that a fire truck is parked in front of a building as shown in the figure The beacon light on top of the fire truck is located 13 feet from the wall and has a light on each side If the beacon light rotates 1 revolution every 2 seconds then a model for determining the distance d in feet that the beacon of light is from point A on the wall after t seconds is given by d t 13 tan at Complete parts a through e below tit 2 k is an odd integer Explain what this means in terms of the beam of light on the wall Choose the correct answer below O A When the function is undefined the light is shining on every point on the wall O B When the function is undefined the light is not shining completely on the wall OC When the function is undefined there is no light shining on the wall When the function is undefined the beam of light is shining on exactly one point on the wall 13 ft A

Consider the following loan scenario for Questions 36 through 39 300 000 10 25 Years 2 726 Monthly Loan Amount Interest Rate Term to Maturity Monthly Debt Service Frequency Debt Paid What would be the loan balance for the beginning of month two end of month one 300 000 O 297 500 O 294 000 299 774

ZZZ Y N N Y N Y N N N N No Bad No True Mask N Y Y N N No Bad Smokes Height 175 Yes No N N N Y N Bad Yes Good Yes Ears Yes Good There exists a consistent tree for this training data i e one that classifies all training points correctly Z Z N N Y N N 176 185 140 170 179

Explore the Subtracting Blocks eManipulative and then investigate this problem The picture below represents the number 52 If you wanted to model the problem 52 17 what would you need to do O A Convert 1 long into 10 cubes OB Take away 7 cubes OC Take away 1 long OD All of the above

Find the corner points of the feasible region of the linear programming problem 10 Maximize z 3x 4y subject to x y 6 2x y 8 x 0 y 0 The feasible region is given below ofy 4 2 2

Homework HW A One must always move upward or to the right on the grid shown below how many paths are there from A to B B Question 8 1 3 15 How many paths are there from A

The graph of f x and g x is given below Use the graph to find f g 0 and g f 3 f x 5 4 3 2 41 f g 0 Soek g f 3 V 4 3 2 1 2 3 4 5 g x 1 2 3 4 X

The graphs of y2r and y 4 z are shown below These two graphs split the plane into 4 regions which we will call Regions A B C and D 1001 92 VS 22 y S 2r 92 4 z 22 4 z 22 y s y s D Match each of the following systems of inequalities with the region shown above A C y 2r B y 4 x

2 Random samples of two first year students two second year studer year students and two fourth year students each from four dormitories were asked to rate on a scale from 1 poor to 10 excellent the quality of the dormitory environment for studying The results are shown in the table Your First Second Third Fourth Donitory A Dormitory B Dormitory C Dormitory D 75 86 98 99 68 55 78 76 68 659 54 74 67 75 89 78 67 Carry out the analysis of variance and prepare the ANOVA table Use a 0 05 6 What can you say concerning the H hypotheses

Find a vector g so that if F i that if F F co C C2 g 0 00 co C C2 C3 then F F g 0 30 20 cz

Determine f where f t is periodic with the given period Also graph f t f t t 0 t 3 and f t has period 3 Determine f f s

X 4 23 V 1 12 Z n x n What is the graphical representation of

5 a b A hockey team has 23 players on it consisting of 13 forwards 7 defensemen and 3 goalies The team charity golf tournament is coming up and 8 players are required to play Determine the probability that exactly 3 defensemen are chosen to play in the golf tournament Determine the probability that at least one goalie will play in the golf tournament

x t cos 4 t 2cos 2 t 3 What are the Fourier series coefficients of this signal

Use A to decode the cryptogram A 3 3 1 2 2 7 9 4 1 3 19 50 37 33 67 5 2 18 4 1 23 21 25 17

y t 9 E2x t x ht a t eu t b 8 t etu t t c 8 t e ult t d 8 t tu t e e 8 t e u t 24

6 Solve the traveling salesman problem for this graph by determining a Hamilton circuit with minimum total distance 10pts 3 F Start point 8 5 5 E B 2 3 Answer

Find gof a g f a for each a E Student Id Student Id Student Score 1001 1002 1013 1015 1016 1021 1023 1030 75 45 90 70 65 80 53 86 y 10 8 7 6 5 4 I 1 ceiling function Answer 3 2 1 Grade Table A B C D F g Student Score y Student Score g Student Score Average of Student Score x6

The pure expectations theory or the expectations hypothesis asserts that long term interest rates can be used to estimate future short term interest rates Based on the pure expectations theory is the following statement true or false The pure expectations theory assumes that a one year bond purchased today will have the same return as a one year bond purchased five years from now False O True The yield on a one year Treasury security is 5 3800 and the two year Treasury security has a 6 4560 yield Assuming that the pure expectations theory is correct what is the market s estimate of the one year Treasury rate one year from now Note Do not round your intermediate calculations 7 543 9 5796 6 4116 8 599 Recall that on a one year Treasury security the yield is 5 3800 and 6 4560 on a two year Treasury security Suppose the one year security does not have a maturity risk premium but the two year security does and it is 0 45 What is the market s estimate of the one year Treasury rate one year from now Note Do not round your intermediate calculations 7 5647

10 Perpetuities Perpetuities are also called annuities with an extended or unlimited life Based on your understanding of perpetuities answer the following questions Which of the following are characteristics of a perpetuity Check all that apply A perpetuity is a series of regularly timed equal cash flows that is assumed to continue indefinitely into the future The present value of a perpetuity is calculated by dividing the amount of the payment by the investor s opportunity interest rate In a perpetuity returns in the form of a series of identical cash flows are earned A perpetuity continues for a fixed time period Your grandfather wants to establish a scholarship in his father s name at a local university and has stipulated that you will administer it As you ve committed to fund a 15 000 scholarship every year beginning one year from tomorrow you ll want to set aside the money for the scholarship immediately At tomorrow s meeting with your grandfather and the bank s representative you will need to deposit rounded to the nearest whole dollar so that you can fund the scholarship forever assuming that the account will earn 4 50 per annum every year Oops The bank representative just reported that he misquoted the available interest rate on the scholarship s account Your account should earn 7 00 The amount of your required deposit should be revised to relationship between the This suggests there is interest rate earned on the account and the present value of the perpetuity

y 2 June 2023 0 0 Maximize subject to 16 04 0 p 2x y x y2 35 x 2y 60 2x y 60 X 25 0 y 0

A company makes color television sets It produces a bargain set that sells for 330 profit and a deluxe set that sells for 590 profit On the assembly line the bargain set requires 5 hours while the deluxe set takes 7 hours The cabinet shop spends 1 hour on the cabinet for the bargain and 2 hours on the cabinet for the deluxe set Both sets require 4 hours for testing and packing On a particular production run the company has available 3600 work hours on the assembly line 900 work hours in the cabinet shop and 2600 work hours in the testing and packing department Complete parts a through c a How many sets of each type should the company produce to maximize profit What is the maximum profit The company should produce deluxe sets and bargain sets to maximize profit Tyne whole numbers

A company produces two types of can openers manual and electric Each requires in its manufacture the use of two machines A and B Each manual can opener require the use of machine A for 2 hours and machine B for 1 hour An electric can opene requires 1 hour on A and 2 hours on B Furthermore suppose the maximur numbers of hours available per month for the use of machines B are 90 6 respectively The profit on a manual can opener is 1 5 and on an electric ca opener it is 2 If the company can sell all the can openers it can produce how mar of each type should it make in order to maximize the monthly profit n order to solve this linear programming problem answer the following questions

del te Maximize z s t 8x1 X1 4x1 X1 482 2x2 3x2 3x2 6X3 3x3 2X3 3x4 3X4 X4 X4 985 X5 3X5 180 270 180 resource 1 resource 2 resource 3 Xj 0 j 1 2 3 4 5 It is known that the basic variables in the optimal solution are X3 X1 X5 a Using this information please identify the optimal solution decision variables and t optimal z value using the formulas for computing the optimal tableau from the initial LP i Section 6 2 of the textbook entitled Some Important Formulas 10 points b Find the dual of this LP 10 points c Determine shadow prices for the three resources using Dual Theorem 10 points d Let c4 be the coefficient of x4 in the objective function given above Using the Du Theorem please determine for what values of c4 will the current basis remain optimal Doints

Jse the simplex algorithm to solve the following LP Maximize z 2x1 x2 3X1 X 6 X X 4 X 0 X urs s t

Consider the Primal problem max 2 60r 84x2 72x3 subject to 31 7x2 3x3 10 2x1 2x2 6x3 4 I1 I2 I3 20 a Write the Dual problem b Solve the Dual problem by graphical method c Then solve the Primal problem by using Complementary Slackness Theorem

Find the maximum value of P 7a 13y 47 given the following constraints y 1 21 7y 35 The maximum at

Now substitute the functions R x 371x and C x 71x 3 300 into P x R x C x Simplify the result by collecting like terms P x R x C x P x 371x

Q1 Truckco manufactures two types of trucks 1 and 2 Each truck must go through the painting shop and assembly shop If the painting shop were completely devoted to painting Type 1 trucks then 800 per day could be painted if the painting shop were completely devoted to painting Type 2 trucks then 700 per day could be painted If the assembly shop were completely devoted to assembling truck 1 engines then 1 500 per day could be assembled if the assembly shop were completely devoted to assembling truck 2 engines then 1 200 per day could be assembled Each Type 1 truck contributes 300 to profit each Type 2 truck contributes 500 Formulate an LP that will maximize Truckco s profit

When considering market research the first step is to review recent secondary dat True False

If a screw measures 4 eighths inch in diameter what size hole must a washer have in order to be 0 009 inch larger than the screw

A manufacturer uses activity based costing to assign overhead cost to products Budgeted cost Information for its activities follow Budgeted Cost Activity Purchasing 135 000 Activity Cost Driver Purchase orders Square feet Factory services Setup Setups Compute an activity rate for each activity Round your answers to 2 decimal places Activity Purchasing Factory services Setup Budgeted Cost 135 000 32 000 65 000 s 32 000 65 000 Budgeted Activity Usage purchase orders square feet setups Budgeted Activity Usage 4 500 purchase orders 5 000 square feet 50 Setups Activity Rate per purchase order per square foot per setup

1 point Which of the following graphs have hamiltonian circuits S K T L E N G F H H I H D J E C B D 72

1 point Consider the graph shown below A B D E C F H Give an example of a Hamiltonian path in the graph shown above T G

1 point Are the following statements true or false 1 If a complte graph has an Euler circuit then the graph has an odd number of vertices 2 If a graph has an Euler trail but not an Euler circuit then every Euler trail must start at a vertex of odd degree 3 Every bipartite graph has an Euler circuit and n are both even 4 If Km n has an Euler circuit then m 5 Every graph with an Euler trail is connected Note In order to get credit for this problem all answers

Find a differential operator that annihilates the given function e5x 12ex A differential operator that annihilates 5x 12ex is Type the lowest order annihilator that contains the minimum number of terms Type your answer in factored or expanded form

Watch help video Company X tried selling widgets at various prices to see how much profit they would make The following table shows the widget selling price x and the total profit earned at that price y Write a quadratic regression equation for this set of data rounding all coefficients to the nearest tenth Using this equation find the profit to the nearest dollar for a selling price of 15 5 dollars Price x 15 25 17 50 23 50 33 25 39 25 42 50 Profit y 18020 24158 33611 34906 23526 16285 Copy Values for Calculator Open Statistics Calculator Regression Equation

Question 12 C Identify the numbers labeled with the letters A B and C on the scale below 7 000 A Letter A represents the number Letter B represents the number 48 000 Letter C represents the number Question Help Worked Example 1 B H Q

There are two similar triangles in the diagram Find the unknown measurement X 240 P 720 80 Q

DATE CLASS Directions Look at the two figures Draw the LINE OF REFLECTION between them 1 Draw the LINE OF REFLECTION 3 Draw the LINE OF REFLECTION 2 Draw the LINE OF REFLECTION 4 Draw the LINE OF REFLECTION

Which of the given line of code is useless to the program include stdio h include math h include stdlib h int main float x 0 y 0 z 0 a 0 printf Enter value scanf f a while a 0 X X 1 y y printf Enter value scanf f a z x y rand y printf f n z return 0 A include stdio h B include math C All are important D include stdlib h

7 5 points Solve Poissons Equations v u 2 x y At selected points knowing the boundary values using the grid values shown in the Figure y 3y y 3 P12 P 11 P 0 21 u 0 3 1 5 u y 1 5y x

find c s t P S c 0 95 if X n u 12 n 6 X 11 10

6 The buyers are obtaining a loan of 115 000 in purchasing their new home The interest rate is 8 25 The settlement date is June 13 and the buyers have be told that their first monthly payment is not due until August 1 Which of the following is true a There will be a charge of 447 95 to the sellers for July interest b There will be a debit of 448 02 to the buyers for July interest c The September payment will be a balloon payment covering interest for July August and September d The September payment will cover interest for July and August

HIT governance has the responsibility to ensure transparency and education True False

The National Coordinator for HIT is responsible for implementing Meaningful Use standards True False

Given a right triangle with tan 0 value of the other trigonometric ratios of 0 1 sin 0 2 cos 0 3 sec 0 4 csc 0 5 cot 0 4 determine the Use exact notation not decimal approximations If you need to write a number such as 3 type out