# Finding a linear demand function and maximizing profit

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.

Please see the attachment.

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#### Solution Preview

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) ...

#### 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.