A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below.
Hours required by
Operation A B Hours
Cutting 3 4 48
Welding 2 1 36
The decision variables are defined as:
xi = the amount of product i produced
yi = 1 if xi > 0 and 0 if xi = 0
A spreadsheet implementation of the problem is shown below.
What is the objective function for this problem?
a. Maximize: 17x1 + 21x2 - 60y1 - 80y2
b. Minimize: 60y1 + 80y2
c. Minimize: 17x1 + 21x2 - 60y1 - 80y2
d. Maximize: 17x1 + 21x2

The objective function of the given problem is 17x1 + 21x2 - 60y1 - 80y2. The x represents the selling price of the two products while y represents the units of the two products. The company should create a combination of two products which will maximize the profit.

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andromache andromache · Answer 2 · 2022-03-18T19:06:26+01:00

a. The objective function for the given problem is Maximize : 17x1 + 21x2 - 60y1 - 80y2

Calculation of the objective function:

The objective function should be 17x1 + 21x2 - 60y1 - 80y2.

Here x represents the selling price of the two products while on the other hand, y represents the units of the two products. The company should develop a combination of two products where the profit should be maximized.

Therefore, the correct option is a.

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