Formulation of linear problem

Question

I'd like to ask you how to formulate this problem as linear problem (equations)?

Marie wants to buy oranges and apples. She has to buy at least 5 oranges and the number of oranges has to be less than 2 times number of apples. One orange weights 150 g and one apple weights 100 g. She can't take more than 3600 g of fruits. One orange costs 70 cents, one apple costs 90 cents. How much she can spend the most?

Thanks.

score 2 · Accepted Answer · answered Apr 06 '14 at 07:26

I shall try to go from your words to equations and I shall note $O$ the number of oranges and $A$ the number of apples Marie will buy.

Your first sentence says that Maries has to by at least $5$ oranges; this translates to $$O \geq 5$$ It also says that the number of oranges has to be less than $2$ times number of apples; this translates to $$O \lt 2 \times A$$ Now the total weight of the fruits must be lower than $3600$ grams; similarly, this translates to $$150 \times O + 100 \times A \leq 3600$$ Now, you want that Marie spends all her money and the total price of the fruit is given by $$Cost = 0.70 \times O + 0.90 \times A$$ which you want to maximize, all the previous constraints being satisfied.

Thank you! So that the standard form with slack variables will be: $O - s_1 = 5$, $O -2\times A + s_2 = 0$ and $150\times O + 100\times A + s_3 = 3600$? — kmaci, Apr 06 '14 at 09:04
@kmaci. You are welcome ! What you wrote is correct. Cheers. — Claude Leibovici, Apr 06 '14 at 09:10

Formulation of linear problem

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