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# Optimization problem

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A factory manufactures two types of gadgets, regular and premium. Each gadget requires the use of two operations, assembly and finishing, and there are at most 120 hours available for each operation. A regular gadget requires 1 hour of assembly and 2 hours of finishing, while a premium gadget needs 2 hours of assembly and 1 hour of finishing. Due to other restrictions, the company can make at most 70 gadgets a day.

(a) Define the variables (x and y) for this problem, and state the objective function.

(b) State the constraints for this problem, i.e. enter the inequality for each restriction. Hint: there are 5 constraints.

(c) Find the corner points of the feasibility region. Hint: there are 5 corner points.

(d) Use the objective function and the corner points to find the numbers of each gadget type that should be manufactured each day in order to maximize profit.

Jul 6, 2022

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Let x be the number of regular gadgets, and let y be the number of premium gadgets.  Then the profit is maximized when (x,y) = (40,30).

Jul 6, 2022