A company makes designer sunglasses and when the price is $150, they sell at a r

Question

A company makes designer sunglasses and when the price is $150, they sell at a rate 25 pair each month. However, for every $10 drop in price, the company finds demand will increase by 5 pair per month.

a.) What revenue does the company make if the price remains at $150 for each pair of sungalsses?

b.) What revenue does the company make it the price is dropped to $140 for each pair of sunglasses?

c.) Write a formula for the revenue as a function of x, where x is an increment in both the price and demand.

d.) Find the derivative of the revenue with respect to change in x and then find the value of x that will maximize revenue.

e.) What price will maximize revenue? What is the demand and what is the revenue at this price?

Explanation / Answer

a

Monthly Revenue = 150*25 = $ 3750

b)

Monthly revenue = 140*(25+5) = $ 4200

c)

If price = 150 - 10x, the demand will be 25 + 5x

Revenue = (150 - 10x)*(25 + 5x)

R = -50x^2 + 500x + 3750

d)

dR/dx = -50*(2x) + 500

For max. revenue we put dR/dx = 0

Thus, -50*2x + 500 = 0

x = 5

e)

Price = 150 - 10*5 = $100

Demand = 25 + 5*5 = 50

Revenue = 100*50 = $ 5000

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