The cost, in dollars, to produce x vats of ice cream is C(x)...

The cost, in dollars, to produce x vats of ice cream is C(x) = 2x + 9. When selling them to ice cream shops, the price-demand function, in dollars per vat, is p(x) = 82 - 2x. Find the profit function. P(x) = How many vats of ice cream need to be sold to maximize the profit. Select an answer Find the maximum profit. Select an answer Find the price to charge per vat to maximize profit. Select an answer

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Transcript

00:01 Okay, first we determine the profit function.

00:04 So we write profit function p of x equals the revenue function minus the cost function.

00:17 And the revenue function which is written as r of x.

00:21 Cost function is c of x.

00:24 Revenue function is basically x times the price demand function.

00:29 So we write x times of p of x gives revenue function minus the cost function c of x.

00:35 So let's replace p of x by 82 minus 2x.

00:40 So therefore this becomes x times of 82 minus 2x.

00:45 And minus of the cost function is 2x plus 9.

00:49 So i write down this in brackets 2x plus 9.

00:53 Let's simplify this to determine the profit function.

00:56 We distribute this x.

00:58 So we get 82x minus 2x times x is minus 2x squared.

01:06 Is minus 2x minus 9 if we distribute the minus we can simplify this we have 82x minus 2x these two are like terms so first i write down this negative 2x squared then 82x minus 2x is plus 80x and then minus 9 so this basically represents the profit function p of x we now determine the number of wads of ice cream needed to be sold to maximize the profit so basically we have to maximize the profit.

01:45 We have to determine the x so that the profit is maximum.

01:49 So let's consider the profit function p of x.

01:53 This equals negative to x squared plus 80x minus 9...

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