The Badminton Company has 4,000 machine hours available annually to manufacture racquets. The following information is available for the two different racquets produced by Badminton: How many units of each racquet should be manufactured for the company to maximize its operating income?

Question

The Badminton Company has 4,000 machine hours available annually to manufacture racquets. The following information is available for the two different racquets produced by Badminton:  How many units of each racquet should be manufactured for the company to maximize its operating income?

Quizplus · Accepted Answer

The first step is to calculate the contribution margin per unit for each racquet.

- Pro racquet: 
Sales price = $150
Variable cost per unit = $70 + ($30/50) * 50 = $100 
Contribution margin per unit = Sales price - Variable cost per unit = $50

- Mid racquet: 
Sales price = $80
Variable cost per unit = $40 + ($20/40) * 40 = $60
Contribution margin per unit = Sales price - Variable cost per unit = $20

Next, we need to determine how many units of each type of racquet should be produced to maximize operating income. We can use the following formula:

Contribution margin per unit * Number of units = Total contribution margin

Let's start with the Mid racquet:

- Maximum number of Mid racquets that can be produced with 4,000 machine hours = 4,000 / 0.5 = 8,000 units 
- Total contribution margin for 8,000 Mid racquets = $20 * 8,000 = $160,000

Now let's move on to the Pro racquet:

- Maximum number of Pro racquets that can be produced with 4,000 machine hours = 4,000 / 1 = 4,000 units 
- Total contribution margin for 4,000 Pro racquets = $50 * 4,000 = $200,000

To maximize operating income, we should produce as many units of the product with the higher contribution margin per unit (Pro racquet) as possible while staying within our total available machine hours. Based on the calculations above, we can produce 4,000 Pro racquets and still have 4,000 - 4,000 = 0 machine hours left.

Therefore, the answer is B: 2,000 units of Pro and 500 units of Mid, which will result in a total contribution margin of $220,000.

The Badminton Company Has 4,000 Machine Hours Available Annually to Manufacture