The Scrod Manufacturing Co. produces two key items: special-purpose Widgets (W) and more generally useful Frami (F). Management wishes to determine that mix of W & F which will maximize total profits (P)
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Data
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W
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F
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Unit profit contributions
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$30
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$20
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Demand estimates (unit/week)
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250
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500
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Average processing rates - each product requires processing on both machines (units/hour)
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Machine 1
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2
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4
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Machine 2
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3
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3
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The two products compete for processing time using the same limited plant capacity. Only 160 hours are available on each of two machines (1 and 2) during each week, barring unexpected equipment breakdowns. Management has established a desired minimum production level of 200 units per week (total output: W + F) in order to maintain distribution outlets.
As a newly hired management analyst for Scrod, you have been asked to analyze the available options and recommend an appropriate product mix. Your boss has suggested that you structure a model of the underlying constrained optimization problem and test to be sure that a feasible solution exists before proceeding to analyze the alternatives.
You do not have to solve this problem; just set it up and make sure that a feasible solution exists. You should try this both with and without the demand estimates included as constraints.
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