Suppose that the cost of making a pound cake is 5 and demand

Suppose that the cost of making a pound cake is $5 and demand for this cake is d(p)=100-10p, if 0<=p<=10 on a given day. Compute the total margin maximizing price.

must show work

Solution

Cost of pound cake = 5 $

Demand of the cake d(p) = 100-10p where p is the price.

Revenue = (100-10p)*p

Cost =(100-10p)*5

Profit margin = (Revenue - Cost)/Revenue = (100-10p)*(p-5)/(100-10p)*5 = (p-5)/5

Total margin maximizing price (p) = 10 $ to ensure maximum profit margin in the case above whiich is 100%