## Question

Maximize P = 5x + 4y

subject to 3x + 5y ≤ 61

4x +y ≤ 19

x ≥ 0; y ≥ 0

The maximum is P = _____ at (x, y) = ( ______ )

Solve the linear programming problem by the simplex method.

Maximize P = 19x + 18y

subject to x + y ≤ 12

3x + y ≤ 30

10x + 7y ≤ 70

x ≥ 0; y ≥ 0

The maximum is P = _____ at (x, y) = ( ______ )

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 $9/unit of Product A and a profit of 310/unit of Product B.

To manufacture 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture 1 unit of Product B requires 9 min on Machine I and 4 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?

Product A units

Product B units

What is the largest profit the company can realize?

$

Is there any time left unused on the machines? (If so, give the number of minutes remaining. If not, enter o.)

Machine I min

Machine II min

Kane Manufacturing has a division that produces two models of hibachis, model A and model B. To produce each model A hibachi requires 6 lb of cast iron and 12 min of labor. To produce each model B hibachi requires 7 lb of cast iron and 6 min of labor. The profit for each model A hibachi is $7, and the profit for each model B hibachi is $6.50. If 2200 lb of cast iron and 40 labor-hours are available for the production of hibachis each week, how many hibachis of each model should the division produce each week to maximize Kane's profit?

model A hibachis

model B hibachis

What is the largest profit the company can realize?

$

Is there any raw material left over? (If so, give the amount remaining. If not, enter o.)

cast iron lb

labor labor-hr

A financier plans to invest up to $975,000 in two projects. Project A yields a return of 10% on the investment, whereas Project B yields a return of 15% on the investment. Because the investment in Project B is riskier than the investment in Project A, the financier has decided that the investment in Project B should not exceed 40% of the total investment. How much should she invest in each project to maximize the return on her investment?

Project A $

Project B $

What is the maximum return?

$

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