ANSWER ALL QUESTIONS PLEASE.

1// Solve the linear programming problem by the method of corners. Maximize P = x + 4y subject to x + y 9 2x + y 12 x 0, y 0 FIND P = x = y =

2// Solve the linear programming problem by the method of corners. Maximize P = 4x 3y subject to x + 4y 12 2x + y 10 x 0, y 0 FIND P = x = y =

3// Solve the linear programming problem by the method of corners. Maximize P = 3x + 7y subject to 3x + y 24 3x + 4y 33 y 6 x 0, y 0 FIND P = x = y =

4// Solve the linear programming problem by the method of corners. Minimize C = 2x + 3y subject to x + y 7 x + 4y 19 x 0, y 0 FIND C = x = y =

5// Solve the linear programming problem by the method of corners. Maximize P = 4x - 3y subject to x + 2y 44 5x + 4y 133 2x + y 22 y 2, x 0 FIND P = x = y =

6// A company manufactures two products, A and B, on two machines, I and II. It has been determined that the company will realize a profit of $3/unit of product A and $5/unit of product B. To manufacture a unit of product A requires 11 min on machine I and 7 min on machine II. To manufacture a unit of product B requires 19 min on machine I and 11 min on machine II. There are 5 hr of machine time available on machine I and 3 hr of machine time available on machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit? model A units model B units What is the optimal profit? $

7// National Business Machines manufactures two models of fax machines: A and B. Each model A costs $100 to make, and each model B costs $140. The profits are $29 for each model A and $40 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2100 and the company has earmarked no more than $540,000/month for manufacturing costs, how many units of each model should National make each month in order to maximize its monthly profit? model A units model B units What is the optimal profit? $

8// A finance company has a total of $30 million earmarked for homeowner and auto loans. On the average, homeowner loans have a 10% annual rate of return, whereas auto loans yield a 12% annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans. Determine the total amount of loans of each type that Madison should extend to each category in order to maximize its returns. housing million dollars automobile million dollars What are the optimal returns? million dollars

9// A financier plans to invest up to $400,000 in two projects. Project A yields a return of 10% on the investment, whereas project B yields a return of 16% on the investment. Because the investment in project B is riskier than the investment in project A, she has decided that the investment in project B should not exceed 35% of the total investment. How much should the financier invest in each project in order to maximize the return on her investment? project A $ project B $ What is the maximum return? $