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Optimizing Widget and Gadget Production for Maximum Profit

Calculate the production quantities of widgets and gadgets to maximize profits based on daily demands and production capabilities. By analyzing constraints and graphing feasible regions, determine the ideal production levels for maximum income.

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Optimizing Widget and Gadget Production for Maximum Profit

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  1. Max And Amy’s Math Thing Widget=x 1200>x>500 Gadget=y 1400>y>700 x+y>2300 Situation: A manufacturer makes widgets and gadgets at least 500 widgets and 700 gadgets are needed to meet the minimum daily demands. A machine can produce 1200 widgets and 1400 gadgets per day. If the company sells widgets for $ 0.40 and gadgets for $ 0.50 each, how many of each item should be produced for maximum income? Profit= $0.40x+$0.50y $830= .40(1200)+.50(700) $1030=.40(1200)+.50(1100) $1060=.40(900)+.50(1400) $550=.40(500)+.50(700) $900=.40(500)+.50(1400)

  2. Summary To find the maximum profit of widgets and gadgets we began by listing all constraints that we found. After listing constraints, we graphed the constraints and found the feasible region and important points. Once we found this, we substituted the x and the y values in the objective function to find the maximum profit and the minimum profit. We discovered that when x is 900 and y is 1400, the profit will be the most.

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