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 constraint for the budget is represented by A)$35A + $25B $3,000. C)$12A + $8B $3,000. D)$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 constraint for the budget is represented by A)$35A + $25B < $3,000. B)$35A + $25B > $3,000. C)$12A + $8B > $3,000. D)$12A + $8B < $3,000.

Quizplus · Accepted Answer

The budget constraint can be represented as follows:
Cost of producing A = $12 per unit (from the resource requirement chart)
Cost of producing B = $8 per unit (from the resource requirement chart)
Let's say TicToc produces x units of A and y units of B. Then the total cost will be:
Cost = (12x) + (8y)
Since TicToc has a budget of $3000 per week, the budget constraint is:
(12x) + (8y) ≤ 3000
This is equivalent to:
3x + 2y ≤ 750
Now, let's consider the profit:
Profit per unit of A = $35
Profit per unit of B = $25
Let's say TicToc produces x units of A and y units of B. Then the total profit will be:
Profit = (35x) + (25y)
TicToc wants to maximize its profit, subject to the budget constraint:
Maximize (35x) + (25y) subject to 3x + 2y ≤ 750
One way to solve this problem is to use linear programming. The optimal solution turns out to be:
x = 125 (produce 125 units of A)
y = 0 (do not produce any units of B)
The maximum profit is:
Profit = (35*125) + (25*0) = $4375
Therefore, the best choice is D: 12A + 8B < 3000.

TicToc Produces Product a and Product B