ou are given a linear programming problem. Maximize      P = 3x + 3y subject to   5x  +  3y  ≤  30      Resource 1   2x  +  3y  ≤ 21   Resource 2       x  ≤ 4   Resource 3       y  ≥ 0         x  ≥ 0   (a) Use the method of corners to solve the problem. The maximum is P =  at  (x, y) =              . (b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution.  ≤ c ≤  (c) Find the range of values that Resource 1 can assume.  ≤ (Resource 1) ≤  (d) Find the shadow price for Resource 1.

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Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.