A company has determined that the price and the monthly dema

A company has determined that the price and the monthly demand of one of its products are related by the equation D = rootsquare (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 10 units 15 units 20 units 25 units which of the following values of D represents the breakeven point 10 units 15 units 20 units 25 units

Solution

D= (400-p)^1/2

take square on both sides

D^2 = 400-p

P=400-D^2

Total revenue = D*P=D*(400-D^2) = 400D-D^3

Total cost = 1125+100D

Profit (P) = total revenue - total cost = 400D-D^3-1125-100D = 300D-D^3-1125

dP/dD = 0

300-3D^2=0

D=10 UNITS

Breakeven point:

Company breakeven point will be when

P=0

300D-D^3-1125=0

solve for D

I will put all option values and try

so i get answer of 15 units, lets put it in equation

300D-D^3-1125=0

(300*15)-(15)^3-1125=0

4500-3375-1125=0

4500-4500=0

0=0

So 15 units is the right answer.