Question

1.) The demand model p=0.02x+19 gives the price per model (in dollars per novel) p when novels are sold. The cost (in dollars) for publishing x novels is given by C(x)=4x+19.

a.)How many novels should be sold in order for revenue to be a maximum?

b.)What is the maximum profit?

c.) Find the average cost when 50 novels are sold.

Answer 1

demand function is p=-0.02x+19

revenue function is given by

compare this function with

here we have

x coordinate of the vertex is

475 novels should be sold for maximum revenue  

.

.

.

.

profit function is given by

compare this function with

here we have

x coordinate of the vertex is

.

maximum profit is $2793.5

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.

.

.

an average cost function is given by

take x=50

the average cost for 50 novels is $4.38