Based on the following labor/material/costs/revenue structure, develop a production plan to maximize profit. You have 40 hours per week at the shown rate at each position type and can plan on 15% additional hours at overtime rates of 150%. You have room for a total of 8 positions (V through Z) – employees are only assigned to one position. All positions (employees) will be paid for at least 40 hours per week. At least 1 unit of each product (A through F) must be made.

Question

Based on the following labor/material/costs/revenue structure, develop a production plan to maximize profit. You have 40 hours per week at the shown rate at each position type and can plan on 15% additional hours at overtime rates of 150%. You have room for a total of 8 positions (V through Z) – employees are only assigned to one position. All positions (employees) will be paid for at least 40 hours per week. At least 1 unit of each product (A through F) must be made.

Positions/Products
A B C D E F Cost/Each
V 5 0 2 0 7 3 25.00
W 3 3 4 2 0 0 28.00
X 4 2 2 3 3 0 30.00
Y 0 5 4 3 2 3 32.00
Z 4 3 0 2 3 4 35.00

Material
1 1.2 .8 .7 1.25 .7 100.00

Revenue/Each
703 613 525 468 651 466

Answer 1

To develop a production plan to maximize profit, we need to consider the labor and material costs as well as the revenue for each product.

First, let's calculate the total labor and material costs for each position and product combination. Multiply the number of units of each product by the labor cost for each position, and then multiply the result by the material cost for each product.

For example, for position V and product A, the total cost would be:
(5 units * $25/unit) + (1 unit * $1.2/unit) = $128

Now, let's calculate the revenue for each product by multiplying the number of units produced by the revenue per unit.

For example, for product A, the revenue would be:
5 units * $703/unit = $3,515

Next, we need to consider the available hours of labor. We have 40 hours per week for each position, and we can plan for 15% additional hours at overtime rates of 150%. This means we can allocate a maximum of 46 hours per week for each position.

To maximize profit, we need to find the combination of positions and products that generates the highest profit. We can do this by comparing the profit for each combination.

Profit = Revenue - Total Cost

Calculate the profit for each combination and choose the combination with the highest profit.

For example, for position V and product A:
Profit = ($3,515 - $128)

Repeat this calculation for all position and product combinations and choose the combination with the highest profit.

Make sure to assign at least one unit of each product to meet the requirement.

Once you have identified the combination with the highest profit, you can develop a production plan by assigning the positions to the corresponding products.