A company produces product A and product B.These products have the following resource requirements. The firm has a weekly production budget of $5000 and a maximum of 800 hours of labor per week.Each A produced generates $45.00 in profit for the company.Each B produced generates $35.00 in profit for the company.The labor constraint is represented by A)45A + 35B 800. C)4A + 5B 800. D)4A + 5B

Question

A company produces product A and product B.These products have the following resource requirements. The firm has a weekly production budget of $5000 and a maximum of 800 hours of labor per week.Each A produced generates $45.00 in profit for the company.Each B produced generates $35.00 in profit for the company.The labor constraint is represented by A)45A + 35B < 800. B)45A + 35B > 800. C)4A + 5B > 800. D)4A + 5B < 800.

Quizplus · Accepted Answer

The labor constraint is represented by the equation: 
4A + 5B ≤ 800 (since the company cannot exceed 800 hours of labor per week)

The profit generated by each product is: 
Profit from A = $45.00 
Profit from B = $35.00

The objective is to maximize profit while staying within the constraints.

Let's use the graphical method to find the optimal solution.

Step 1: Plot the constraints on a graph.

To plot the labor constraint, we can rewrite it in terms of B: 
B ≤ (800 - 4A)/5

We can plot this constraint by finding two points on the line:

When A = 0, B = 160 (800/5)

When A = 200, B = 120 [(800-4(200))/5]

Plotting these two points and drawing a line joining them, we get:

https://i.imgur.com/HlNyYcU.png

We can see that the feasible region (the shaded region) is bounded by the x-axis, y-axis, and the labor constraint.

Step 2: Find the corner points of the feasible region.

The corner points are the intersections of the lines that form the boundaries of the feasible region. In this case, we have three corner points:

(0,0), (0,160), and (200,120)

Step 3: Calculate the profit at each corner point.

At (0,0): Profit = 45A + 35B = 0 
At (0,160): Profit = 45A + 35B = 5600 
At (200,120): Profit = 45A + 35B = 10700

Step 4: Choose the corner point with the highest profit.

Based on our calculations, the optimal solution occurs at (200,120), where the company produces 200 units of A and 120 units of B per week, generating a profit of $10700 per week.

Therefore, the answer is D: 4A + 5B < 800.

A Company Produces Product a and Product B