The demand equation for a product is given by x=5000-5p, where is the number of units produced and sold at price p(in dollars) per unit. The cost (in dollars)

Question

producing x units is given by unit. The cost (in dollars) of producing x units is given by C(x)=4x+12000. Express each of the following as a function of price. 

a. Cost

b.Revenue

c.Profit

Answer 1

x = 5000 - 5p

 

Cost = 4x + 12,000

Revenue = xp

Profit = Revenue - Cost

 

Substitute 5000 - 5p for x

 

Cost = 4(5000 - 5p) + 12000 = 20,000 - 20p + 12,000 = 32,000 - 20p

Revenue = xp = (5000-5p)p = 5000p - 5p²

Profit = Revenue-Cost = 5000p - p² - 32,000 + 20p = -p² + 5020p - 32,000