TicToc produces product A and product B. These products have the following resource requirements. The firm has a weekly production budget of $3000 and a maximum of 1000 hours of labor per week. Each A produced generates $35.00 in profit for the company. Each B produced generates $25.00 in profit for the company. The capacity constraint for labor is

Question

TicToc produces product A and product B. These products have the following resource requirements.  The firm has a weekly production budget of $3000 and a maximum of 1000 hours of labor per week. Each A produced generates $35.00 in profit for the company. Each B produced generates $25.00 in profit for the company. The capacity constraint for labor is

Quizplus · Accepted Answer

To solve this problem, we need to use the resource constraints and the profit equations to come up with a linear programming model.
Let A be the number of units of product A produced and B be the number of units of product B produced.
The resource constraint for labor is given as a maximum of 1000 hours per week, which translates to the inequality:
4A + 3B ≤ 1000
The production budget constraint is:
35A + 25B ≤ 3000
The profit equation is:
Profit = 35A + 25B
We want to maximize profit, subject to the resource and budget constraints. Therefore, this problem can be formulated as follows:
Maximize Z = 35A + 25B
Subject to the resource constraint: 4A + 3B ≤ 1000
And the budget constraint: 35A + 25B ≤ 3000
We can solve this using graphical or algebraic methods. The optimal solution occurs at the intersection of the two constraints, which is (A, B) = (200, 133.33).
Therefore, the best choice is C, 4A + 3B < 1000, which is the correct resource constraint to use in the linear programming model.

TicToc Produces Product a and Product B