Formulaic an Integer Program that could be used to answer the following question

Question

Formulaic an Integer Program that could be used to answer the following question. Ihawlit trucking company is deciding how many of each type of product to pack into a truck for shipping to a neighboring stale. There are k different types of products, each with weight w_i, volume v_i, and estimated profit p_i. Assume that, there is an unlimited supply of each type of product. Also assume that any combination of products can he packed into the truck as long as the total weight does not exceed W and the total volume does not exceed the volume of the truck V. How many of each product should Ihawlit pack into the truck in order to maximie profit?

Explanation / Answer

There are two constraints for this problem

Let the number of items vary from a1 to ak for eah product, then the constratins are

a1w1 + a2w2 + a3w3 + ... + akwk <= W

a1v1 + a2v2 + a3v3 + ... + akvk <= V

Profit Function

Z = a1p1 + a2p2 + ... + akpk

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