A ceramics store manufactures and sells coffee mugs. The revenue r(x) from the sale of x coffee mugs is given by r(x)-6.5x. Suppose the function for the cost of manufacturing x coffee mugs is c(x)= 0.75x + 1850. A. Find the profit on 500,1000, and 5000 coffee mugs. B. Write the Profit Function

Step-by-step explanation:

The revenue r(x) from the sale of x coffee mugs is given by

r(x) = 6.5x

the function for the cost of manufacturing x coffee mugs is c(x)= 0.75x + 1850.

Profit = Revenue - cost

P(x) = r(x) - c(x)

P(x) = 6.5x - (0.75x + 1850)

P(x) = 6.5x - 0.75x - 1850

P(x) = 5.75x - 1850

A) profit when x = 500 is

P = 5.75 × 500 - 1850

P = 2875 - 1850

P = 1025

profit when x = 1000 is

P = 5.75 × 1000 - 1850

P = 5750 - 1850

P = 3900

profit when x = 5000 is

P = 5.75 × 5000 - 1850

P = 28750 - 1850

P = 26900

B) The profit function would be

P(x) = r(x) - c(x)

P(x) = 5.75x - 1850

See picture attached:)

Hope that makes sense! If you'd like any more help with maths, I'd be happy to offer online tuition. You can find me at: www.birchwoodtutors.com