A company produces two kinds of products. A product of the first type requires 1/4 hours of assembly labor, 1/8 hours of testing, and $1.2 worth of raw materials. A product of the second type requires 1/3 hours of assembly, 1/3 hours of testing, and S0.9 worth of raw materials. Given the current personnel of the company, there can be at most 90 hours of assembly labor and 80 hours of testing each day. Products of the first and second type have a market value of S9 and S8 respectively.

(a) Formulate a linear program that maximizes the daily profit of the company

(b) Write the standard form of the LP you formulated in part (a)

(c) Consider the following modification to the original problem: Suppose that up to 50 hours of overtime assembly labor can be scheduled, at a cost of $7 per hour. Cant be easily incorporated into the linear programming formulation and how?

Question

Business

Sienna Kaufman

23 February, 22:38

A company produces two kinds of products. A product of the first type requires 1/4 hours of assembly labor, 1/8 hours of testing, and $1.2 worth of raw materials. A product of the second type requires 1/3 hours of assembly, 1/3 hours of testing, and S0.9 worth of raw materials. Given the current personnel of the company, there can be at most 90 hours of assembly labor and 80 hours of testing each day. Products of the first and second type have a market value of S9 and S8 respectively.

(a) Formulate a linear program that maximizes the daily profit of the company

(b) Write the standard form of the LP you formulated in part (a)

(c) Consider the following modification to the original problem: Suppose that up to 50 hours of overtime assembly labor can be scheduled, at a cost of $7 per hour. Cant be easily incorporated into the linear programming formulation and how?

+4

Answers (1)

Know the Answer?

Skyler Hays · Answer 1

295 units of Qa

and 129 untis of Qb

Explanation:

1/4Assembly hours x Qa + 1/3Assembly hoursx Qb = ASH

1/8 testing hours x Qb + 1/3 testing hours x Qb = TSH

Profit = 9 x Qa + 8 x Qb

Assembly hours < = 90

testing hours < = 80

We also has to make the cosntrain that units should be integer as we cannot do half a unit.

We build this in solver to get the max profit.

A B C D

Units Assembly Testing Profit

295 0.25 0.125 9

129 0.125 0.33 8

89.88 79.88 3,687.00

(295 x 0.25 + 129 x 0.125)

(295 x 0.125 + 129 x 0.33)

(295 x 9 + 129 x 8)