Your Initials: mpuny produces and sells a consumer product and is able to contro

Question

Your Initials: mpuny produces and sells a consumer product and is able to control the demand for the product by varying the selling price. The approximate relationship between price and demand is: 1. A co p = 38 + (27001) for D2I Where p is the price per unit in dollars and D is the demand per month. The company is seeking to maximize its profit. The total cost equation is $1000+D (20 points) a) Determine the value of D per month that maximizes profir? (5 pts) b) What is the associated maximum profit per month for D found in (a)? (5 pts) c) What is the unit price for the value found in (a)? (5 pts) d) Find the break even points? (5 pts)

Explanation / Answer

The given inverse demand function is p=38+(2700/D)

The total cost equation is C=1000+D^2

(a) Total revenue (TR) =p*D=(38+(2700/D))*D=38D+2700

Marginal revenue (MR)= d(TR)/dD=38

Marginal cost (MC) = dC/dD=2D

For profit maximization MR=MC

38=2D. Thus the profit maximizing output is D=19

(b) Total revenue when D=19 is found by substituting D=19 in TR=38D+2700

So total revenue=3422

Total cost when D=19 is found by substituting D=19 in  C=1000+D^2

so taotal cost= 1361

Thus profit= Total revenue-total cost=3422-1361=2061

(c) The unit price is found by substituting D=19 in the inverse demand function  p=38+(2700/D)

Thus unit price p= 38+(2700/19)=180.1

(d) The break even point is the point at which total revenue=total cost

38D+2700=1000+D^2

Solving the above quadratic equation we get the value D=64

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