Answer to Question #283246 in Financial Math for Usman ali

Question

manufacturer of microcomputer produces three different models. The following table summarizes wholesale process, material cost per unit and labor cost per unit. Annual fixed costs are $ 25 million.

Microcomputer

Model 1

Model 2

Model 3

Wholesale price per unit

$500

$1,000

$1,500

Material cost per unit

$175

$400

$750

Labor cost per unit

$100

$150

$225

Determine a joint total revenue function for sale of the three different microcomputer models?

Determine an annual total cost function for manufacturing the three models.

Determine the profit function for sales of the three models.

Answer 1

$$\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Microcomputer }$$ $$\def\arraystretch{1.5} \begin{array}{c:c:c:c} & Model\ 1 & Model\ 2 & Model\ 3 \\ \hline Wholesale\\ price/unit & \$500 & \$1000 & \$1500 \\ \hdashline Material\\ cost/unit & \$175 & \$400 & \$750 \\ \hdashline Labor\\ cost/unit & \$100 & \$150 & \$225 \\ \hdashline \end{array}$$

1. A joint total revenue functions for sale of the three different microcomputer models are:

$$TR_1 = 500Q_1,$$

$$TR_2 = 1000Q_2,$$

$$TR_3 = 1500Q_3.$$

A joint total revenue function for sale of the three different microcomputer models is

$$TR=TR_1+TR_2+TR_3$$

$$=500Q_1+1000Q_2+1500Q_3$$

2. An annual total cost functions for manufacturing the three models:

$$TC_1 = 25000000/3+(175+100)Q_1,$$

$$TC_2= 25000000/3+(400+150)Q_2,$$

$$TC_3= 25000000/3+(750+225)Q_3.$$

$$TC=TC_1+TC_2+TC_3$$

$$=25000000+275Q_1+550Q_2+975Q_3$$

3. The profit function for sales of the three models is

$$TP=TP_1 +TP_2+TP_3$$

$$=TR-TC$$

$$=500Q_1+1000Q_2+1500Q_3$$

$$-(25000000+275Q_1+550Q_2+975Q_3)$$

$$=225Q_1+450Q_2+525Q_3-25000000$$