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TV AND VCR PRODUCTION Ali Longwell Cole Guffey

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The Situation: A company manufactures TVs and VCRs. It must produce at least 20 TV sets per month, but cannot make more than 60 of them. The company also can produce more than 100 VCRs month. Total production of TVs and VCRs combined cannot exceed 140. The profit for a TV set is $45 and $175 for a VCR. Find the number of each item that should be manufactured in order to maximize profit.

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Constraints x0 y0 x20 x60 y100 x+y140 y140-x x= TVs y= VCRs We want to maximize the profit!

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OBJECTIVE FUNCTION PROFIT= 45x + 175y We want to maximize the profit! $45 per each TV $175 for each VCR

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GRAPH 20 40 60 80 100 120 140 160 0 Feasible Reason VERTICES: (60,0) (20,0) (20,100) (40,100) (60,80) Maximum Profit for TV and VCR Production

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To Find the Maximum Profit… Objective Function: Profit=45x + 175y (60,0): Profit=45(60) + 175(0) Profit= $2700 (20,0): Profit=45(20) + 175(0) Profit= $900 (20,100): Profit=45(20) + 175(100) Profit= $18400 (40,100): Profit=45(40) + 175(100) Profit= $19300 (60,80): Profit=45(60) + 175(80) Profit= $16700 MAXIMUM PROFIT:

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summary In order to maximize the TV and VCR Production companys profits they would have to sell 40 TV sets and 100 VCRs. By graphing the restraints you can find the feasible region, doing this you find 5 vertices. Of these points, the point (40,100) gives you the highest profit of $19300.

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Linear Programming. What is linear programming? Use a system of constraints (inequalities) to find the vertices of the feasible region (overlapping shaded.

Linear Programming. What is linear programming? Use a system of constraints (inequalities) to find the vertices of the feasible region (overlapping shaded.

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