MATHEMATICAL APPLICATIONS FOR THE MGT
MATHEMATICAL APPLICATIONS FOR THE MGT
12th Edition
ISBN: 9780357865095
Author: HARSHBARGER
Publisher: CENGAGE L
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Chapter 14, Problem 31RE
To determine

To calculate: The number of units of each product, 1 and 2, that will maximize the profit and the maximum profit where the weekly profit (in dollars) from a sale of two products is given by P=40x+80yx2y2, where x is the number of units of product 1 and y is the number of units of product 2.

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a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? x1 12 23 81 82 83 S4 $1 -20 1 1 0 0 0 3 82 3 0 -2 0 1 2 0 6 12 1 1 -3 0 0 1 0 2 84 -3 0 2 0 0 -1 1 4 2 -2 0 11 0 0 -4 0 -8 b) Solve the following linear program using the 2-phase simplex algorithm. You should give the initial tableau and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. maximize 21 - - 2x2 + x3 - 4x4 subject to 2x1+x22x3x4≥ 1, 5x1+x2-x3-4 -1, 2x1+x2-x3-342, 1, 2, 3, 4 ≥0.
Suppose we have a linear program in standard equation form maximize c'x subject to Ax=b, x≥ 0. and suppose u, v, and w are all optimal solutions to this linear program. (a) Prove that zu+v+w is an optimal solution. (b) If you try to adapt your proof from part (a) to prove that that u+v+w is an optimal solution, say exactly which part(s) of the proof go wrong. (c) If you try to adapt your proof from part (a) to prove that u+v-w is an optimal solution, say exactly which part(s) of the proof go wrong.
(a) For the following linear programme, sketch the feasible region and the direction of the objective function. Use you sketch to find an optimal solution to the program. State the optimal solution and give the objective value for this solution. maximize +22 subject to 1 + 2x2 ≤ 4, 1 +3x2 ≤ 12, x1, x2 ≥0 (b) For the following linear programme, sketch the feasible region and the direction of the objective function. Explain, making reference to your sketch, why this linear programme is unbounded. maximize ₁+%2 subject to -2x1 + x2 ≤ 4, x1 - 2x2 ≤4, x1 + x2 ≥ 7, x1,x20 Give any feasible solution to the linear programme for which the objective value is 40 (you do not need to justify your answer).

Chapter 14 Solutions

MATHEMATICAL APPLICATIONS FOR THE MGT

Ch. 14.1 - Prob. 9ECh. 14.1 - Prob. 10ECh. 14.1 - Prob. 11ECh. 14.1 - Prob. 12ECh. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.1 - Prob. 16ECh. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - Prob. 18ECh. 14.1 - Prob. 19ECh. 14.1 - Prob. 20ECh. 14.1 - Prob. 21ECh. 14.1 - In Problems 15-22, evaluate each function as...Ch. 14.1 - Prob. 23ECh. 14.1 - Prob. 24ECh. 14.1 - 25. Curve speeds One method traffic planners use...Ch. 14.1 - Prob. 26ECh. 14.1 - Prob. 27ECh. 14.1 - Prob. 28ECh. 14.1 - 29. Mortgage The following tables show that a...Ch. 14.1 - 30. Wind chill Wind and cold temperatures combine...Ch. 14.1 - Prob. 31ECh. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.1 - Prob. 34ECh. 14.1 - Prob. 35ECh. 14.1 - 36. Profit The Kirk Kelly Kandy Company makes two...Ch. 14.1 - Prob. 37ECh. 14.1 - Prob. 38ECh. 14.2 - Prob. 1CPCh. 14.2 - Prob. 2CPCh. 14.2 - Prob. 3CPCh. 14.2 - Prob. 4CPCh. 14.2 - Prob. 5CPCh. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Prob. 12ECh. 14.2 - Prob. 13ECh. 14.2 - Prob. 14ECh. 14.2 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 - 19. Find the slope of the tangent in the...Ch. 14.2 - 20. Find the slope of the tangent in the...Ch. 14.2 - Prob. 21ECh. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - Prob. 27ECh. 14.2 - Prob. 28ECh. 14.2 - Prob. 29ECh. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - 32. If , find the following. (a) (b) (c) (d) Ch. 14.2 - 33. If , find the following. Ch. 14.2 - 34. If , find the following. Ch. 14.2 - Prob. 35ECh. 14.2 - Ch. 14.2 - Ch. 14.2 - Prob. 38ECh. 14.2 - Prob. 39ECh. 14.2 - Prob. 40ECh. 14.2 - 41. . Ch. 14.2 - . Ch. 14.2 - Prob. 43ECh. 14.2 - Ch. 14.2 - 45. Mortgage When a homeowner has a 25-year...Ch. 14.2 - 46. Mass transportation ridership Suppose that in...Ch. 14.2 - 47. Wilson's lot size formula In economics, the...Ch. 14.2 - 48. Cost Suppose that the total cost (in dollars)...Ch. 14.2 - 49. Pesticide Suppose that the number of thousands...Ch. 14.2 - 50. Profit Suppose that the profit (in dollars)...Ch. 14.2 - Prob. 51ECh. 14.2 - Prob. 52ECh. 14.2 - 53. Production Suppose that the output Q (in...Ch. 14.2 - Prob. 54ECh. 14.2 - Prob. 55ECh. 14.2 - Prob. 56ECh. 14.3 - CHECKPOINT If the joint cost in dollars for two...Ch. 14.3 - Prob. 2CPCh. 14.3 - Prob. 3CPCh. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - 3. The total cost of producing 1 unit of a product...Ch. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14.3 - 9. If the joint cost function for two products is ...Ch. 14.3 - 10. Suppose the joint cost function for x units of...Ch. 14.3 - 11. Suppose that the joint cost function for two...Ch. 14.3 - Prob. 12ECh. 14.3 - Prob. 13ECh. 14.3 - Prob. 14ECh. 14.3 - Prob. 15ECh. 14.3 - Prob. 16ECh. 14.3 - Prob. 17ECh. 14.3 - Prob. 18ECh. 14.3 - Prob. 19ECh. 14.3 - Prob. 20ECh. 14.3 - 21. Suppose the Cobb-Douglas production function...Ch. 14.3 - Prob. 22ECh. 14.3 - Prob. 23ECh. 14.3 - Prob. 24ECh. 14.3 - Prob. 25ECh. 14.3 - Prob. 26ECh. 14.3 - Prob. 27ECh. 14.3 - Prob. 28ECh. 14.3 - Prob. 29ECh. 14.3 - Prob. 30ECh. 14.4 - CHECKPOINT Suppose that Find Ch. 14.4 - Prob. 2CPCh. 14.4 - Prob. 3CPCh. 14.4 - Prob. 4CPCh. 14.4 - Prob. 1ECh. 14.4 - Prob. 2ECh. 14.4 - Prob. 3ECh. 14.4 - Prob. 4ECh. 14.4 - Prob. 5ECh. 14.4 - Prob. 6ECh. 14.4 - Prob. 7ECh. 14.4 - Prob. 8ECh. 14.4 - Prob. 9ECh. 14.4 - Prob. 10ECh. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - 19. Profit Suppose that the quarterly profit from...Ch. 14.4 - Prob. 20ECh. 14.4 - 21. Nutrition A new food is designed to add weight...Ch. 14.4 - Prob. 22ECh. 14.4 - 23. Production Suppose that tons is the...Ch. 14.4 - 24. Production Suppose that x units of one input...Ch. 14.4 - 25. Profit Suppose that a manufacturer produces...Ch. 14.4 - Prob. 26ECh. 14.4 - Prob. 27ECh. 14.4 - Prob. 28ECh. 14.4 - 29. Profit A company manufactures two products, A...Ch. 14.4 - Prob. 30ECh. 14.4 - Prob. 31ECh. 14.4 - The manager of the Sea Islands Chicken Shack is...Ch. 14.4 - Prob. 33ECh. 14.4 - Prob. 34ECh. 14.4 - Prob. 35ECh. 14.4 - Prob. 36ECh. 14.5 - Prob. 1CPCh. 14.5 - Prob. 2CPCh. 14.5 - Prob. 3CPCh. 14.5 - Prob. 4CPCh. 14.5 - Prob. 1ECh. 14.5 - Prob. 2ECh. 14.5 - Prob. 3ECh. 14.5 - Prob. 4ECh. 14.5 - Prob. 5ECh. 14.5 - Prob. 6ECh. 14.5 - Prob. 7ECh. 14.5 - Prob. 8ECh. 14.5 - Prob. 9ECh. 14.5 - Prob. 10ECh. 14.5 - Prob. 11ECh. 14.5 - Prob. 12ECh. 14.5 - Prob. 13ECh. 14.5 - Prob. 14ECh. 14.5 - Prob. 15ECh. 14.5 - 16. Utility Suppose that the budget constraint in...Ch. 14.5 - 17. Utility Suppose that the utility function for...Ch. 14.5 - 18. Utility Suppose that the utility function for...Ch. 14.5 - Prob. 19ECh. 14.5 - Prob. 20ECh. 14.5 - 21. Cost A firm has two plants, X and Y. Suppose...Ch. 14.5 - Prob. 22ECh. 14.5 - Prob. 23ECh. 14.5 - Prob. 24ECh. 14.5 - 25. Manufacturing Find the dimensions (in...Ch. 14.5 - Prob. 26ECh. 14 - 1. What is the domain of ? Ch. 14 - Prob. 2RECh. 14 - Prob. 3RECh. 14 - 4. If . Ch. 14 - Prob. 5RECh. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - Prob. 14RECh. 14 - In Problems 15-18, find the second partials. Ch. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - Prob. 19RECh. 14 - Prob. 20RECh. 14 - Prob. 21RECh. 14 - Prob. 22RECh. 14 - Prob. 23RECh. 14 - Prob. 24RECh. 14 - Prob. 25RECh. 14 - Prob. 26RECh. 14 - Prob. 27RECh. 14 - Prob. 28RECh. 14 - Prob. 29RECh. 14 - Prob. 30RECh. 14 - Prob. 31RECh. 14 - Prob. 32RECh. 14 - Prob. 33RECh. 14 - Prob. 34RECh. 14 - 35. Modeling US. average wage The table gives the...Ch. 14 - Prob. 36RECh. 14 - Prob. 1TCh. 14 - Prob. 2TCh. 14 - Prob. 3TCh. 14 - Prob. 4TCh. 14 - Prob. 5TCh. 14 - Prob. 6TCh. 14 - 7. Suppose the demand functions for two products...Ch. 14 - Prob. 8TCh. 14 - 9. Find x and y that maximize the utility function...Ch. 14 - Prob. 10T
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