Question

XYZ Co. produces two products, Product A and Product B. Product A is sold at $115 and Product B is sold at $145. To produce one unit of Product A, it costs the company a total of $75. Also, to produce one unit of Product B, it costs the company a total of $85. In the last year, XYZ Co.'s total cost of production was $80,000. During the next year, it is expected that the company will only have 45,000 hours of production time available, while all other production factors remain the same. Product A requires 12 hours to produce one unit, and Product B takes double the time that of Product A to produce one unit. XYZ Co. would like to draw a production plan in which the profits would be maximized for the upcoming year.

Determine the production plan where XYZ Co. would be maximizing profits, where * sales expectations for Product A is 2300 units and for Product B it is 1200.

Answer 1

XYZ Co. must determine an optimal mix of Product A and Product B to maximize profits within the 45,000-hour production time constraint. They should prioritize production based on the profit per hour for each product and adjust the production to meet the sales expectations without exceeding the available time.

Step-by-step explanation:

The student's question involves determining the optimal production plan for XYZ Co. to maximize profits considering the given constraints of production time and sales expectations. Product A takes 12 hours to produce and generates a profit of $40 per unit, while Product B takes 24 hours to produce and generates a profit of $60 per unit.

Given that the available production time for the next year is 45,000 hours and the sales expectations are 2300 units for Product A and 1200 units for Product B, the following production plan can be suggested:

• Produce all 2300 units of Product A: 2300 units * 12 hours/unit = 27,600 hours
• Produce all 1200 units of Product B: 1200 units * 24 hours/unit = 28,800 hours

The total required production time is 56,400 hours, which exceeds the available 45,000 hours. Therefore, XYZ Co. would have to adjust the production mix by reducing the number of Product B units and potentially increasing Product A until the available time is fully utilized.

These figures suggest that the production plan should focus on the optimal mix of Product A and B that fits within the 45,000-hour constraint, while also considering the sales expectations and the profit per unit.

To maximize profits within the available time, the company should calculate the profit per hour for each product (Product A: $40/12 hours, Product B: $60/24 hours) and prioritize the production of the product with the higher profit per hour ratio until the sales expectation is met or the production time is exhausted. Adjustments should be made to ensure the production time is not exceeded and the expected sales volumes are met as closely as possible.

Answer 2

The profit-maximizing production plan for XYZ Co. involves producing and selling all 1200 units of Product B, and producing and selling 2300 units of Product A, if possible, within the 45,000 production hours available.

Step-by-step explanation:

To find the profit-maximizing production plan for XYZ Co., we need to calculate the profit for each product and see how many units of each product can be produced within the available production hours. Profit per product is sales price minus cost of production:

• Product A: $115 - $75 = $40 profit per unit
• Product B: $145 - $85 = $60 profit per unit

Given that:

• Product A requires 12 hours per unit
• Product B requires 24 hours per unit (double that of Product A)
• There are 45,000 production hours available
• Sales expectations are 2300 units for Product A and 1200 units for Product B

To maximize profits, XYZ Co. would want to produce and sell the maximum number of the most profitable product (Product B) that they can within the constraints of the expected sales and production hours:

1. Calculate the maximum number of units of Product B that can be produced in 45,000 hours: 45,000 / 24 = 1875 units.
2. Since the sales expectation for Product B is only 1200 units, XYZ Co. can produce all 1200 units within approximately 28,800 hours (1200 units x 24 hours per unit).
3. This leaves 16,200 production hours available for Product A (45,000 - 28,800).
4. Calculate the number of units of Product A that can be produced in 16,200 hours: 16,200 / 12 = 1350 units.
5. However, since the sales expectation for Product A is 2300 units, XYZ Co. would produce and sell all 2300 units using 27,600 hours (2300 units x 12 hours per unit), provided that sales could be increased beyond the expectation.

Thus, the profit-maximizing production plan, under the sales expectations, would be to produce and sell 1200 units of Product B and 2300 units of Product A, if sales can be expanded for Product A.