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L02_Graphical Solution of two variables

# L02_Graphical Solution of two variables - Proble 6 Proble S...

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Problem 6 Problem Set 2.3A Page 26 (Modified) Electra produces two types of electric motors, each on a separate assembly line. The respective daily capacities of the two lines are 150 and 200 motors. Type I motor uses 2 units of a certain electronic component, and type II motor uses only 1 unit. The supplier of the component can provide 400 pieces a day.The profits per motor of types I and II are \$8 and \$5 respectively. Formulate the problem as a LPP and find the optimal daily production.

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Let the company produce x 1 type I motors and x 2 type II motors per day. 1 2 8 5 z x x = + Subject to the constraints 1 2 1 2 1 2 150 200 2 400 , 0 x x x x x x + The objective is to find x 1 and x 2 so as to Maximize the profit
We shall use graphical method to solve the above problem. Step 1 Determination of the Feasible solution space The non-negativity restrictions tell that the solution space is in the first quadrant. Then we replace each inequality constraint by an equality and then graph the resulting line (noting that two points will determine a line uniquely).

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Next we note that each constraint line divides the plane into two half-spaces and that on one half-space the constraint will be ≤ and on the other it will be ≥. To determine the “correct” side we choose a reference point and see on which side it lies.
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L02_Graphical Solution of two variables - Proble 6 Proble S...

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