Linear Programming
1. A beverage cans manufacturer makes 3 types of soft drink cans needed for the beverage producers to fill soft drinks of three different volumes. The maximum availability of the machines' time allotted per day is 90 hours and the supply of metal is limited to 120 kg per day. The following table provides the details of the input needed to manufacture one batch of 100 cans.
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Cans
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|
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Large
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Medium
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Small
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Maximum
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Metal (kg)/batch
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9
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6
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5
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120
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Machines' Time (hr)/batch
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4.4
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4.2
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4
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90
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Profit/batch
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$50
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$45
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$42
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Let L = number of Large cans produced
M = number of Medium cans produced
S = number of Small cans produced
Formulate and solve for the recommended production quantities for all the three different types cans by maximizing the profit. Use Excel solver to find your answers. Report the optimal value of L
2. Based on question 1, use Excel Solver to find the optimal solution and report the value of M.
3. Based on question 1, use Excel Solver to find the optimal solution and report the value of S.
4. Based on question 1, use Excel Solver to find the optimal solution and report the optimal value of the objective function.
5. Based on question 1, write down the objective fuction.
1. A soft drink manufacturing company has 3 factories set up one in each of the three cities - Orland, Tampa, and Port St. Lucie and it supplies the produced soft drink bottles to 3 warehouses located in the city of Miami. The associated per-unit transportation cost table is provided below:
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Transportation Costs ($)
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Factories/Warehouse (W)
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W1
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W2
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W3
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Orlando
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4
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3
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7
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Tampa
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7
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6
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4
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Port St. Lucie
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3
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6
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6
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The factory at Orlando has a capacity of 15,000 units.
The factory at Tampa has a capacity of 18,000 units.
The factory at Port St. Lucie has a capacity of 8,000 units.
The requirements of the warehouses are:
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Transportation Costs ($)
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Factories/Warehouse (W)
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W1
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W2
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W3
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Orlando
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4
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3
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7
|
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Tampa
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7
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6
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4
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Port St. Lucie
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3
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6
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6
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How many decision variables do you have in this problem?
7. A soft drink manufacturing company has 3 factories set up one in each of the three cities - Orland, Tampa, and Port St. Lucie and it supplies the produced soft drink bottles to 3 warehouses located in the city of Miami. Using the information from question 6 answer the following:
How many constraints do you have in this problem? (ignore the sign constraints)
8. Based on the problem of the soft drink manufacturing company:
What is the optimal minimum cost for this problem? Use Excel Solver to find your solution.
9. Based on the problem of the soft drink manufacturing company:
What is the optimal value for the route Orlando - W1, that is how many units should be sent from Orlando to location W1 in order to minimize the total transportation cost?
10. Based on the problem of the soft drink manufacturing company:
What is the optimal value for the route Orlando - W2, that is how many units should be sent from Orlando to location W2 in order to minimize the total transportation cost?
11. Based on the problem of the soft drink manufacturing company:
What is the optimal value for the route Tampa - W1, that is how many units should be sent from Tampa to location W1 in order to minimize the total transportation cost?
12. Based on the problem of the soft drink manufacturing company:
What is the optimal value for the route Tampa - W2, that is how many units should be sent from Tampa to location W2 in order to minimize the total transportation cost?
13. Based on the problem of the soft drink manufacturing company:
What is the optimal value for the route Port St. Lucie- W3, that is how many units should be sent from Port St. Lucie to location W3 in order to minimize the total transportation cost?
14. Three plants P1, P2, and P3 of a gas corporation supply gasoline to three of their distributors in the city located at A, B, and C locations. The plants' daily capacities are 4500, 3000, and 5000, gallons respectively, while the distributors' daily requirements are 5500, 2500, and 4200 gallons. The per-gallon transportation costs (in $) are provided in the table below:
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Distributor
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Plant
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A
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B
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C
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P1
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0.8
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0.5
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1
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P2
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0.7
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0.65
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0.8
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P3
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0.5
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0.45
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0.7
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What is the optimal minimized cost?
15. Using the sensitivity report in question 14, answer the following:
What is the new minimum cost of transportation if we increase the demand of distributor B to be 2600. Use the shadow price for Demand B in the constraints table to estimate the new cost.