Answer to Question #283245 in Financial Math for Usman ali

Question

A 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.

three models.

What is an annual profit if the firm sells 20,000, 40,000 and 10,000 units, respectively of the three models?

Answer 1

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

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

$$TR_1 = 500Q_1,$$

$$TR_2 = 1000Q_2,$$

$$TR_3 = 1500Q_3.$$

An annual total cost functions for manufacturing the three models:

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

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

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

The profit functions for sales of the three models are:

$$TP_1 =TR_1-TC_1$$

$$= 500Q_1 - (25000000/3 + 275Q_1)$$

$$= 225Q_1 - 25000000/3 ,$$

$$TP_2=TR_2-TC_2$$

$$= 1000Q_2 - (25000000/3 + 550Q_2)$$

$$= 450Q_2 - 25000000/3 ,$$

$$TP_3 =TR_3-TC_3$$

$$= 1500Q_3 - (25000000/3 + 975Q_3)$$

$$= 525Q_3 - 25000000/3.$$

If the firm sells 20,000, 40,000 and 10,000 units, respectively of the three models

$$Q_1=20000, Q_2=40000, Q_3=10000$$

$$TP=TP_1+TP_2+TP_3$$

$$= 225(20000) - 25000000/3$$

$$[phone]) - 25000000/3$$

$$[phone]) - 25000000/3$$

$$=2750000$$

An annual profit if the firm sells 20,000, 40,000 and 10,000 units, respectively of the three models is $2,750,000.