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Published byMyra Julien Modified over 2 years ago

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Stephen Gonzales, Amandeep Tamber, Ross Nakata, Jonathan Gutierrez

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Problem Statement Problem Summary Assumptions Formulation Constraints Input Values Solutions Sensitivity Analysis Report to Manager

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A customer requires during the next four months, respectively, 50, 65, 100, and 70 units of a commodity (no backlogging is allowed). Production costs are $5, $8, $4, and $7 per unit during these months. The storage cost from one month to the next is $2 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 could be sold for $6. Formulate an LP that will minimize the net cost incurred in meeting the demands of the next four months.

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MonthCost of Production/UnitDemand 1$550 2$865 3$4100 4$770

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No inventory at beginning of month Unlimited capacity Other costs in production were ignored

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X t = number of commodities produced each month during month t i t = number of commodities on hand at the end of month t where t=1,2,3,4 for each month in the problem. O.F MINIMIZE COST Z = 5x 1 +8x 2 +4x 3 +7x 4 +2i 1 +2i 2 +2i 3 -6i 4

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1i 1 = 0 + x 1 – 50 2i 2 = i 1 + x 2 – 65 3i 3 = i 2 + x 3 – 100 4i 4 = i 3 + x 3 – 70 5x 1 > 0 6x 2 > 0 7x 3 > 0 8x 4 > 0 9i 1 > 0 10i 2 > 0 11 i 3 > 0 12 i 4 > 0

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Month Units to Produce Productio n Cost per Unit Total Production CostDemand Units Remaining at End of Month Inventory CostTotal Cost 1 115$ 5.00$ 575.005065$ 130.00$ 705.00 2 0$ 8.00$ -650$ - 3 170$ 4.00$ 680.0010070$ 140.00$ 820.00 4 0$ 7.00$ -700$ - GRAND TOTAL $ 1,525.00

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The minimum cost we calculated is $1,525 MonthUnits to Produce DemandUnits Remaining at End of Month 11155065 20 0 317010070 40 0

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Unit Cost of Production Total Cost (All 4 Months)Units to Produce $7.00 and above$1,5250 $2.00 to $6.99$1200 to $1524.3565 Unit Cost of Production Total Cost (All 4 Months)Units to Produce For month 2:

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