Finding a linear demand function and maximizing profit
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You are given two points representing the number of items sold at a particular price. From these two points, a linear demand function is constructed. You are also given information on the cost of each item so that you can construct a cost function. From the demand function you can form a revenue function and finally the profit function is the revenue minus the cost. This profit function can the be maximized by taking the derivative at setting it to zero.
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Solution Summary
You are given two points representing the number of items sold at a particular price. From these two points a linear demand functions is constructed. You are then asked to find the price that will maximize profit using the linear demand function, the cost function, and the revenue function.
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a) First find the linear demand function by fitting a line to two points (5.4, 4000) and (6, 2500).
The slope would be m=(2500-4000)/(6-5.4)=(-1500)/(.6)=-2500
Now use the point slope formula q-2500 = -2500(p -6) ...
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