Question

An electronics company has developed a new hand-held device. The company predicts that the start-up cost to manufacture the new product will be $125,000, and the cost to make one device will be $6.50. A. If the company plans on selling the device at a wholesale price of $9, write and solve an inequality to determine how many must be sold for the company to make a profit. Show your work. B. The cost of making one device is 10% more than the company predicted. What is the new cost of making one device? How many devices must it now sell at the same wholesale price to make a profit? C. Suppose the company wants to start making a profit after selling the same number of devices you found in part A. What should the new wholesale price be? Explain how you found this price.

Answer 1

A) to calculate the break even point we can use the following:

break even point = fixed costs / contribution margin

break even point = 125,000 / (9 - 6.5) = 125,000 / 2.5 = 50,000 units

The company must sell over 50,000 units to make a profit

B) if the unit production costs increase 10%, the new unit cost will be $7.15, and the new break even point will be: 125,000 / (9 - 7.15) = 125,000 / 1.85 = 67,567.6 which we round up to 67,568 units.

Now the company must sell at least 67,568 units to make a profit

C) If the company wants to increase its product price to a level where the break even point is 50,000 units, then the new price should be $9.65.

The contribution margin must be $2.5, so if the production costs are $7.15, we just add $2.5 to get $9.65 per unit.