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appropriate variables

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Jillian Scott sells three items. A, B and C in a gift shop. Each unit of A costs her $5 to buy, $1 to sell and $2 to deliver. For each unit of B, the costs are $3, $2, and $1 respectively, and for each unit of C, the costs are $6. $2, and $5 respectively. The profit on A is $4; on B $3 and on C $3. How many of each should she order to maximize her profit if she can spend $1200 on buying costs, $800 on selling costs, and $500 on delivery costs.

What are the appropriate variables; write the objective functions; write the constraints as inequalities and solve.

Cauchy Canners produce canned corn, beans and carrots. Demand for vegetables requires it to produce at least 1000 cases per month. Based on past sales, it should produce at least twice as many cans of corn as of beans and at least 340 cases of carrots. It costs $10 to produce a case of corn, $15 to produce a case of beans and $25 to produce a case of carrots.

Using the method of surplus variables, find how many cases of each vegetables should be produced to minimize costs. What is the minimum cost?

Using the method of duals, find how many casdes of each vegetable should be produced to minimize costs. What is the minimum cost?

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What are the appropriate variables?

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