A factory manufactures two types of gadgets: regular and premium.

Each gadget requires two stages, assembly, and finishing, and there are at most 120 hours available for each operation (that is, 120 hours for assembly, and 120 hours for finishing).

A regular gadget requires 1 hour of assembly and 3 hours of finishing.

A premium gadget requires 3 hours of assembly and 2 hour of finishing.

The company can make at most 10 gadgets each day.

The company makes $400 pro t for each regular gadget and $550 pro t for each premium gadget.

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

(b) Let x be the number of regular gadgets, and let y be the number of premium gadgets. Enter the inequality for each restriction. Each inequality should be of the form ax + by <= c, where a, b, c are positive integers with no common factor.

(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 nd the numbers of each gadget type that should be manufactured each day in order to maximize profit.

Note: for this assignment, just use the information stated above. However, if you're interested, you can think about whether the above information makes sense or is realistic | it's actually kind of a tricky question in some ways. (This is just for your own interest, you do not have to hand in your thoughts on this as part of the assignment!)

 Jul 21, 2022

The optimal point is (x,y) = (20,50).

 Jul 22, 2022

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