A retailer has been selling 1200 tablet computers a week at...

A retailer has been selling 1200 tablet computers a week at $\$ 350$ each. The marketing department estimates that an addi. tional 80 tablets will sell each week for every $\$ 10$ that the price is lowered. (a) Find the demand function. (b) What should the price be set at in order to maximize revenue?(c) If the retailer's weekly cost function is $$ C(x)=35,000+120 x $$ what price should it choose in order to maximize its profit?

Transcript

00:01 Hi there, so for this problem, we're told that retailer has been selling 1200 tablet computers a week at a price of 350 dollars.

00:13 Now, the marketing department estimates that an additional 80 tablets.

00:17 So, 80 additional table at tables.

00:22 Will each so then.

00:27 We'll sell each week for every 10.

00:30 The price is lower so then if we lower the price to 10.

00:36 Okay.

00:36 So, with this, we can have with this information, we can already have the, um, some information that we can use for the demand function, because this will give us the slow.

00:47 Okay, so remember that the 1st question is to find the demand function.

00:50 So then we know that the slope for that function is just minus 10, because we are decreasing the price divided by 80 and increase in the top.

01:00 So, um, this will give us just minus 1 divided by 8.

01:04 So with that said, we use the following expression for part a.

01:08 So that will be the price that a minus initial price.

01:12 That is 350 this divided by the quantity where you can label as x, then this minus initial quantity.

01:18 That is 1000 and 200.

01:21 This equals to minus 1 divided by 8.

01:23 So now we solve for the price in here.

01:26 So that will give us minus 1 divided by 8.

01:29 Then this times x minus 1000 and 200, then this plus 350.

01:36 So, let's use our calculator in here to simplify this expression.

01:47 Okay, so that will give us minus x divided by 8 plus 500.

01:52 Okay, so that is the demand function now for part b of this problem.

01:57 The question is what should be the price set at an order to maximize the revenue? remember that the revenue is just x times the price.

02:04 So, we substitute the price expression in here.

02:06 So that will give us minus x squared divided by 8 plus 500 times x.

02:11 Now, to minimize it to maximize this with respect to x.

02:15 So, that will give us minus x divided by 4 to this plus 500 and then we set this equal to 0.

02:22 Now we solve for x in here...

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