Write the Constraint Inequalities and the Profit Formula for This

question 52

Essay

Write the constraint inequalities and the profit formula for this linear programming mixture problem: Amazin' Raisin Baking Co. makes both raisin cake and raisin pie. A batch of raisin cakes requires 5 lbs of flour, 2 lbs of sugar, and 1 lb of raisins. A batch of raisin pies requires 2 lbs of flour, 3 lbs of sugar, and 4 lbs of raisins. There are 165 lbs of flour, 110 lbs of sugar, and 120 lbs of raisins available each week. Standing orders require at least five batches of raisin cakes and eight batches of raisin pies per week. If profit on a batch of raisin cakes is $35 and profit on a batch of raisin pies is $40, how many batches of each should be made per week to maximize profit?

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Definitions:

Implicit Costs

The opportunity costs of using resources owned by the firm for its own production rather than earning income elsewhere.

Accounting Profits

The net income reported on the financial statements of a company, calculated as total revenues minus explicit costs and depreciation.

Industry Supply

The total quantity of a specific good or service that all firms in an industry are willing to sell at a given price level.

Demand

The quantity of a good or service that consumers are willing and able to purchase at various prices during a specified time period.