Question

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

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

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3. 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.

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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

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

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4. 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.

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​ 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

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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?

Answer 1

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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