Question

In: Math

To find the optimal solution to a linear optimization problem, do you have to examine all...

  1. To find the optimal solution to a linear optimization problem, do you have to examine all the points in the feasible region? Explain.

  1. Can a linear programming problem have no solution? More than one solution? Explain.

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  1. A beverage can manufacturer makes three sizes of soft drink cans—Small, Medium and Large. Production is limited by machine availability, with a combined maximum of 90 production hours per day, and the daily supply of metal, no more than 120 kg per day. The following table provides the details of the input needed to manufacture one batch of 100 cans for each size.

​

                                                                               Cans

Large

Medium

Small

Maximum

Metal (kg)/batch

9

6

5

120

Machines’ Time (hr)/batch

4.4

4.2

4

90

Profit/batch

$50

$45

$42

​

Develop a linear programming model to maximize profit and determine how many batches of each can size should be produced.

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  1. Gatson manufacturing company produces two types of tires: Economy tires and Premium tires. The manufacturing time and the profit contribution per tire are given in the following table.

​

​

Operation

Manufacturing Time (Hours)

Time Available

Economy tires

Premium tires

Hours

Material Preparation

4/3

1/2

600

Tire Building

4/5

1

650

Curing

1/2

2/4

580

Final Inspection

1/5

1/3

120

Profit/Tire

$12

$10

​

Answer the following assuming that the company is interested in maximizing the total profit contribution.

  1. What is the linear programming model for this problem?
  2. Develop a spreadsheet model and find the optimal solution using Excel Solver. How many tires of each model should Gatson manufacture?
  3. What is the total profit contribution Gatson can earn with the optimal production quantities?

Solutions

Expert Solution

The formula for the spreadsheet is shown below.

The solver parameters are shown below.

The result is shown below. Gatson should manufacture 406 economy tires and 116 premium tires.

(c)

The maximum profit that can be obtained is $6032.

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milcah answered 4 months ago
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