A company looks to maximize its profits a The demand
Last updated: 3/26/2024
A company looks to maximize its profits a The demand function relates the price of a product and the quantity sold Suppose that the company sells 1000 units when the price is 10 dollars and sells 20 fewer units every time the price is increased by one dollar selling the corresponding amount more due to price decreases Find a formula for f p the number of goods sold when the price is p dollars b The revenue is the money the company receives from sales Find a formula for R g p the revenue the company receives when the price is p dollars Hint revenue is the price times the quantity sold c The company can manufacturer goods for a cost of C 1000 2x dollars Find a formula for C h p the cost of producing the number of goods sold when the price is p dollars d The profit is revenue minus cost Find a formula for P j p the profit earned by the company when the price is p dollars What price is a critical number for profit Consider all positive prices p 0 as your domain e Classify the above critical number as corresponding to a local maximum by using a calculator to test nearby values Then argue why this must be the absolute maximum on the domain p 0