Carpet, Inc. is the sole distributor of fine Oriental carpets in the area. The cost of producing and importing one carpet is $1,000. Last year, a total of 3,200 carpets were sold, at a price of $3,000 per unit. This year, they hired a consulting firm (KPMG) which estimated that elasticity of demand for carpets equals -3, and that thedemand for carpets is linear.

A)Construct the demand function. That is, given the information on prices, quantities and price elasticity, give an expression for the demand function.

Hint:Recall that to get a demand curve with this information, use the definition ofa linear demand curve combined with the definition of the priceelasticity of demand.

B)Using this information, can you help Carpet, Inc. choose the optimal price? How many carpets would it sell this year?

C)Before Carpet, Inc. had a chance to rewrite the prices and place the order of carpets, the same consulting company did a survey and concluded thathalfof customers who buy carpet from us would use Carpet, Inc for cleaning services (andthe other halfwould not). The cleaning service has a negligible marginal cost, and it will give Carpet, Inc, $200 in NPV terms (the actual price charged for cleaning is higher, but since it is several years down the road, the NPV less than that, and we assume it is equal to $200). Find the optimal price of carpets in this case.