- To find the optimal solution to a linear optimizationproblem, do you have to examine all the points in the feasibleregion? Explain.
- Can a linear programming problem have no solution? Morethan one solution? Explain.
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- A beverage can manufacturer makes three sizes of softdrink cans—Small, Medium and Large. Production is limited bymachine availability, with a combined maximum of 90 productionhours per day, and the daily supply of metal, no more than 120 kgper day. The following table provides the details of the inputneeded to manufacture one batch of 100 cans for eachsize.
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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 programmingmodel to maximize profit and determine how many batches of each cansize should be produced.
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- Gatson manufacturing company produces two types oftires: Economy tires and Premium tires. The manufacturing time andthe profit contribution per tire are given in the followingtable.
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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 assumingthat the company is interested in maximizing the total profitcontribution.
- What is the linear programming model for thisproblem?
- Develop a spreadsheet model and find the optimalsolution using Excel Solver. How many tires of each model shouldGatson manufacture?
- What is the total profit contribution Gatson can earnwith the optimal production quantities?
