A company has determined that the price and the monthly demand of one of its pro
ID: 2875600 • Letter: A
Question
A company has determined that the price and the monthly demand of one of its products are related by the equation D = Squareroot (400 - p), where p is the price per unit in dollars and D is the monthly demand. The associated fixed costs are $1, 125/month, and the variable costs are $100/unit. Use this information to answer Problems 2-52 and 2-53. Select the closest answer. What is the optimal number of units that should be produced and sold each month? (a) 10 units (b) 15 units (c) 20 units (d) 25 units Which of the following values of D represents the breakeven point? (a) 10 units (b) 15 units (c) 20 units (d) 25 unitsExplanation / Answer
52)
given D=(400-p)
400-p=D2
p=400-D2
total revenue R=p*D
R=(400-D2)*D
R=400D-D3
total cost C=1125 +100D
total profit P =R-C
P=400D-D3-100D-1125
P=300D-D3-1125
for maximum profit dP/dD=0 ,d2P/dD2<0
dP/dD=300-3D2=0
3D2=300
D2=100
D=10
optimum number of units that should be produced and sold each month =10 units
53) for breakeven point profit =0
300D-D3-1125=0
D=15 units
D =15 represents breakeven point