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Could you please help me in solving the problem posted below.

A company uses a raw material to produce two types of products. When processed, each unit of raw material yields 2 units of product 1 and 1 unit of product 2. If x1 units of product 1 are produced, then each unit can be sold for $\$49-x_1,$ if $x_2$ units of product 2 are produced, then each unit can be sold for $\$30-2x_2.$ It costs $\$5$ to purchase and process each unit of raw material.

a) Use LINGO b) What is the most that the company would be willing to pay for an extra unit of raw material?

This problem is from Non-Linear Programming chapter. Thank you, Abhishek Baer

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I don't know about LINGO, but mathematically:

$$ \max (49-x_1) x_1 + (30-x_2) x_2 - 5r$$ $$ \text{s.t.} 2x_1 + x_2 \leq 3r $$

Then part two of your question is the dual variable associated with that constraint.

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