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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.
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