Chul Park & Sons manufacture and sell specialized automotive testing equipment, including alternator testers, solenoid testers, and voltage regulator testers. Over the past 15 years, Chul Park & Sons has established a national reputation as a producer of accurate, reliable, and functional computerized products for testing automotive electrical and electronic components.

Chul Park & Sons, however, is only one of many companies that manufacture automotive testing equipment. Customers can choose from among numerous automotive suppliers, and, as a result, Chul Park & Sons’ sales are quite sensitive to the selling price it sets for each product. Mr. Park currently is working on setting the selling price for his main product, a universal (3 in 1) tester. He believes that the following equation nicely captures the relation between the selling price and demand for his universal tester:

Quantity = 32,500 - (10 × Price)

where Quantity represents the demand for Chul Park & Sons’ universal tester and Price represents the unit selling price established by Mr. Park. Mr. Park also informs you that the variable cost per universal tester is $750 and that the fixed costs associated with producing and selling the universal tester equal $14,000,000 per year.

Required:

a. What is Chul Park & Sons’ expression for annual profit for its universal tester?

b. Determine the price at which Chul Park & Sons maximizes profit on its universal tester. What is the profit on the universal tester at this price?