You are in the process of deciding on the price for a new product. The goal is to maximize the profit. The alternatives are different possible prices...

You are in the process of deciding on the price for a new product. The goal is to maximize

the profit. The alternatives are different possible prices from $2 per unit to $10 per unit. The

model to be used is described below. Let:

X = number of units produced and sold

C(X) = total cost of producing X units

P = price to be charged

NP = total net profit (to be maximized)

Cost relationship: C(X) = 800 + 1.25X

Sales relationship: X = - 100 + 2000/P

Profit relationship: NP = P.X 

–

 C(X)

a. 

Comment on the model in terms of reasonableness of the relationships.

b. 

Find an approximate solution to the model by trial and error (i.e., use several values of

price between $2 and $10, and try to find to a price that gives a good profit. Use of MS

Excel is highly recommended).

c. 

Find the optimum price value by following these steps:

 

Summarize net profit function in terms of price

 

Compute the derivative of the net profit function with respect to the price

 

Set the result equal to zero and solve for the price.