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In the following exercises, solve the given maximum and minimum problems.An architect is designing a rectangular building in which the front wall costs twice as much per linear meter as the other three walls. The building is to cover $1350 \mathrm{m}^{2} .$ What dimensions must it have such that the cost of the walls is a minimum?

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 7

Applied Maximum and Minimum Problems

Derivatives

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All right. So this question were given the fact that we have a box and the box have the volume of 20 cubic feet, and then we're giving a costume, making each side of the box so the bases extra hide its age. So, uh, we need to reduce the amount of money it takes to make this mark. So let's couple e How much makes Jim eight make each part? So the bottom of the box, which is X square, cost 30 cents per square feet. Then we have the top of the box, which is 20 per square feet. Pontiac, sir. Plus, then we're pleasant sides, which had extent Beach. So there's four so four x age, and that costs 10. Right? So we also know that X squared hands h is my volume, which is a 20. So h he goes to Hunty over expert. So that's the question. Actually become service actually become so deposed. Tony, that's 50 square waas, 40 x times 20 over square. So that is 50 x square clothes each 100 over X. If I graphed the out, I should end up with a function that looks like this, and this tells me there is Ah, minimum when possible mean there is a minimal at X equals to chew. No more extra goto actually closer to. And then I can find out the heights so you could actually go to shield my basis two times two and my height is 20. Divide by two times two, which is good apart. So that's two feet times 23 times.

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