$($An investment problem$)$ A client has approached a stockbroker with the following request: invest $$100,000$ for maximum annual income under the three conditions:

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Spread the investment over no more than three different stocks

Put no more than $40$ percent of the money into any one stock

Put a minimum of $$10,000$ into oil stock

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The broker has identified three stocks for the investing the funds. Their estimated annual returns and price per share are shown in the following table:

Stock

Price$/$share

Estimate Annual return$/$share

Oil

$$120$

$$11$

Auto

$$52$

$$4$

Pharmaceutical

$$18$

$$2$

$$

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Formulate & solve a linear programming model to determine the investment so as to maximize the total estimated returns.

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All decision variables:

x$1=$ the share of Oil stock

x$2=$ the share of Auto stock

x$3=$ the share of Pharmaceutical stock

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$6.$ Which of the following is the objective function?

A$.$ Minimize $11$ x$1+4$ x$2+2$ x$3$

B$.$ Maximize $11$ x$1+4$ x$2+2$ x$3$

C$.$ Minimize $2$ x$1+4$ x$2+11$ x$3$

D$.$ Maximize $2$ x$1+4$ x$2+11$ x$3$

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$7.$ Which of the following is a constraint?

A$.120$ x$1+52$ x$2+18$ x$3<100,000$

B$.120$ x$1+52$ x$2+18$ x$3=100,000$

C$.120$ x$1+52$ x$2+18$ x$3>100,000$

D$.120$ x$1+52$ x$2+18$ x$3100,000$

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$8.$ Which of the following is a constraint?

A$.52$ x$2<40,000$

B$.52$ x$240,000$

C$.52$ x$2>40,000$

D$.52$ x$240,000$

E$.52$ x$2=40,000$

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$9.$ Which of the following is a constraint?

A$.120$ x$1<10,000$

B$.120$ x$110,000$

C$.120$ x$1>10,000$

D$.120$ x$110,000$

E$.120$ x$1=10,000$

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$10.$ Which of the following is a constraint?

A$.$ x$1,$ x$2,$ x$3>0$

B$.$ x$1,$ x$2,$ x$30$

C$.$ x$1,$ x$2,$ x$3<0$

D$.$ x$1,$ x$2,$ x$30$

E$.$ x$1,$ x$2,$ x$3=0$