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 A)12A + 8B 1000. B)12A + 8B

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 A)12A + 8B > 1000. B)12A + 8B < 1000. C)4A + 3B < 1000. D)4A + 3B > 1000.

Quizplus · Accepted Answer

To find the capacity constraint for labor, we need to look at the resource requirements for each product.

Product A requires 4 hours of labor per unit produced, and product B requires 3 hours of labor per unit produced. Let's assume we produce x units of product A and y units of product B.

The total labor used would be:
4x + 3y

We know that the maximum labor available per week is 1000 hours, so:
4x + 3y ≤ 1000

Simplifying this inequality, we get:
-3y ≤ -4x + 1000
y ≥ (4/3)x - 333.33

To maximize profit, we want to produce as many units of A and B as possible within our budget constraint. We can set up the following linear programming model:

Maximize 35x + 25y
Subject to:
4x + 3y ≤ 1000
3x + 2y ≤ 750
x, y ≥ 0
35x + 25y = 3000 (budget constraint)

Solving this model, we get x = 142.86 and y = 85.71. This means we should produce approximately 143 units of A and 86 units of B to maximize profit while staying within our resource and budget constraints.

However, to answer the specific question about the capacity constraint for labor, we need to look at the labor constraint above. Since we want to use less than or equal to 1000 hours of labor and not exceed it, we need to use the less than or equal to symbol in the constraint. Therefore, the correct answer is C: 4A + 3B < 1000.

TicToc Produces Product a and Product B