State the linear programming problem in mathematical terms, identifying the objective function and the constraints.A firm makes products A and B. Product A takes 2 hours each on machine L and machine M; product B takes 2 hours on L and 3 hours on M. Machine L can be used for 14 hours and M for 9 hoursProfit on product A is $7 and $6 on B. Maximize profit.OA Maximize 7A+68Subject to: 2A + 2B < 142A+3859AB20OC. Maximize 7A-68Subject to: 2A 202143A 28 20ABSOOB. Maximize 7A 68Subject to: 2A+28s 1434 2859AB20OD. Maximize 6A+78Subject to2A 38 142A-2059A, B20

There are products A and Bprofit on product A = 7 $profit on product B = 6 $Total profit = 7A + 6B

Answered: State the linear programming problem in…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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State the linear programming problem in mathematical terms, identifying the objective function and the constraints. A car repair shop blends oil from two suppliers. Supplier I can supply at most 48 gal with 3.6% detergent. Supplier II can supply at most 66 gal with 3% detergent. How much can be ordered from each to get at most 100 gal of oil with maximum detergent? OA. Maximize 0.030x + 0.036y Subject to: xs48 y≤ 66 x+y≤ 100 OC. Maximize 48x + 66y Subject to: x248 y266 0.036x +0.03y2 100 OB. Maximize 0.036x+0.03y Subject to: 0≤x≤48 0sys 66 x+ys 100 D. Maximize 48x + 66y Subject to: xs48 y≤ 66 0.036x +0.03y ≤ 100
A store store is looking to stock the following: necklaces, bracelets, rings, and earrings. The objective function measuring profit and constraints are given below. Constraint 1 measures display space in units, constraint 2 measurestime to set up the display in minutes. Constraints 3 and 4 are marketing restrictions. Setup an LP program in Tab "#1" and run additional reports (leave reports in your file) in order to answer the following questions.MAX 100X1+120X2+150X3+125X4S.T.1) X1+2X2+2X3+2X4<1082) 3X1+5X2+X4<1203) X1+X3<254) X2+X3+X4>50a. How many necklaces should be stocked?b. Now many bracelets should be stocked?c. How many rings should be stocked?d. How many earrings should be stocked?e. How much space will be left unused?f. How much time will be used?g. By how much will the second marketing restriction be exceeded?h. What is the profit?i. To what value can the profit on necklaces drop before the solution would change?j. By how much can the profit on rings increase…
A manufacturer of refrigerators must ship at least 100 refrigerators to its two warehouses. Each warehouse holds a maximum of 100 refrigerators. Warehouse A holds 40 refrigerators already, while warehouse B has 15 on hand. It costs $10 to ship a refrigerator to warehouse A and $14 to ship one to warehouse B. How many refrigerators should be shipped to each warehouse to minimize cost? Find the objective function and the constraints for the above problem.
A firm manufactures 2 products A and B. The profits are 5$ and 8$ respectively. The firm has 2 machines and below is the required processing time in hours for each machine on each product. Product A В Machines G 6. 8. H 4 Machine G must be operated for at least 48 hours. Hours Available for machine H is 20 hours. Set up an LP problem to maximize profit and solve it graphically.
Sp
macys needs to hire staff at minimum cost. the average monthly salary of a manager is $2400 and the average monthly salary of a clerk is $1100. The company can accommodate up to 45 workers and needs at least 30 to run properly. They must have at least 10 clerks and may have up to 3 clerks for every 2 managers. How many managers and clerks should macys hire to minimize cost. what is the minimum cost? using simplex
Kevin is an auto mechanic. He spends 2 hours when he replaces the shocks on a car and 2 hours when he replaces the brakes. He works no more than 48 hours a week. He routinely completes at least 2 shocks replacements and 6 brake replacements a week. If he charges $400 for labor replacing shocks and $200 in labor for replacing brakes, how many jobs of each type should he complete a week to maximize his income? Kevin should do shock replacements and brake replacements every week to maximize his weekly income.
Find the corner point that gives the optimal solution for the objective profit function.

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