A company is planning to manufacture and sell a new product

A company is planning to manufacture and sell a new product. The operations department estimated manufacturing costs based on the equation.

Cost for a quantity (Q) is $8,000 + $4.00 Q per year

The sales department suggests that the sales will be price sensitive, and equation that relates selling price (P) and the sales volume (Q) will be

Price = $35.00 - 0.02Q

The company bean counters looked at this and agreed – that as the sales increase, the price would fall as expected.. The unit cost would also drop with increased volume..

The bean counting department set a price that they believed would deliver the maximum company profit.

a. What is the target quantity

b. What is the target price per unit

c. What is the target cost per unit

d. What would be the total profit from the sales.

Solution

The bean counting department sets the price that they believe would deliver the maximum company profit.

In order to maximize company profit, they had to produce the profit-maximizing level of output.

Calculating profit-maximizing level of output -

Profit-maximizing level of output is that level of output at which marginal revenue equals marginal cost.

So, we have to first ascertain the MC and MR of concerned product of the given firm.

Total Revenue (TR) = P * Q = (35 - 0.02Q)* Q = 35Q - 0.02Q²

MR = dTR/dQ = d( 35Q - 0.02Q²)/dQ = 35 - 0.04Q

Total Cost (TC) = 8,000 + 4Q

MC = dTC/dQ = d(8,000 + 4Q)/dQ = 4

Equating MR and MC to ascertain profit maximizing level of output -

MR = MC

35 - 0.04Q = 4

0.04Q = 31

Q = 775 units

The profit-maximizng level of output of firm is 775 units.

(a). As firm wants to earn maximum profit and given the cost and price equation its profit maxmizing level of output is 775 units. So, if it wants to earn maximum profit, it must produce 775 units.

Thus, the target quantity for firm is 775 units.

(b). Calculate target price per unit -

This can be calculated by plugging target quantity in to price equation.

Price equation is as follows -

P = 35 - 0.02Q = 35 - 0.02*775 = $19.5

The target price per unit is $19.5.

(c) Calculate target cost per unit -

We have to first calculate the total target cost by plugging value of target quantity into cost equation.

C = 8,000 + 4Q = 8,000 + 4*775 = 8,000 + 3,100 = $11,100

Total target cost is $11,100.

Target cost per unit = Total target cost/Target quantity = $11,100/775 = $14.32

The target cost per unit is $14.32.

(d) Calculate total profit from sales -

TR = 35Q - 0.02Q² = (35*775) - 0.02(775)² = $27,125 - $12,012.5 = $15,112.5

The total target revenue is $15,112.5

Total target cost is $11,100 (from part c).

Total Profit = Total target revenue - Total target cost = $15,112.5 - $11,100 = $4,012.5

The total profit from the sales would be $4,012.5.