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What will it cost to buy ceiling molding to g0 around a rectangular room with The molding costs $1.13 per linear foot length 20 ft and width 15 f?0 A: S45.20 539.55...

Question

What will it cost to buy ceiling molding to g0 around a rectangular room with The molding costs $1.13 per linear foot length 20 ft and width 15 f?0 A: S45.20 539.55 S33.90 S79.10

What will it cost to buy ceiling molding to g0 around a rectangular room with The molding costs $1.13 per linear foot length 20 ft and width 15 f? 0 A: S45.20 539.55 S33.90 S79.10



Answers

Solve. Crown molding is to be installed in a 16 -foot-wide by 20 -foot-long living room. The subcontractor charges $\$4$ per foot to install the molding. What will be the total cost of installing molding for the room?

Okay, here we have a room and we're talking about bolding getting a mold for the room molding would be the outside. So we're talking about the outside of the room and it measures 12 feet by 11 feet, and I guess I should make that with it longer. But anyway, you have 12 feet by 11 feet, and then you gotta also have this three, three feet of doorway that you don't want to put a molding around. So it's gonna be a perimeter problem member perimeters twice the length, plus twice the with us. We go ahead and put those numbers in twice times 12 times, plus two times 11. But here we have to figure out we gotta subtract those three feet would just add that on at the end. Then we have 24 plus 20 to minus three 24 months, plus 22 is 46 46 minus three is 43 feet. So we need to buy 43 feet of the molding. And the molding is, um is $2 foot. So we go 43 times to which is 86 so it would cost you $86 to mold Put molding around that room

Um not only have somebody painting, this is much like the previous problem where now we have the volume of the room is specified. And in this case, I guess I didn't write it down here either. Uh Vienna equals um 6 68 point 25 keeping feet. All right, so um the total cost, so we have paint for the walls and paint for the ceiling. And assuming we're not painting the floor. So the walls, the paint for the walls cost um six cents per square foot. And paint for the ceiling cost 11 cents per square foot. So the total cost of the pain is the cost to paint the ceiling. And then these are the cost to paint the walls. So again, the walls, we have two different sized walls, the um the constraint we can solve for A. And then substitute in here, so we get our total cost is given by this in terms of the Uh one side, 1 side length and the height show. Um We're gonna take the partials with respect to B. And C. And again we get, you know, things coming in here um with the cost of the wall paint cost of the ceiling paint and everything. And so we set those equals zero because we want to minimize this cost, solve for B. And C. And we can um something very similar to the last problem um Where we, in terms of just in generic form, we have these these things here. Um And actually, if you plug this in these into here, you get that A. Is going to be equal to be So for a particular case with these values here, We get that b. equals nine ft, and c equals um 8.25 ft. And take was nine ft also. So basically we have a nine by nine room that is eight quarter feet high, would be the room, the the dimensions of the room. Given a specific volume. That would minimize the cost of our paint and the cost of our paint would then be plugging everything back into here here. Um about $26.73.

All right. So first excuse me first was draw this picture because pictures help a lot. So what I have is this room thistles. 13 thistles. 14. Right here. I have an entryway, which is four. And right here. I have a window. Which is for that can lick in the door and see out the window to see through the house. It's called a shotgun houses, I think. All right. And what we need to know. Yes, we're gonna put molding around it. And it is $4 for each one. And I don't sell partial wards to make sense for the Okay. So what we need to do then, is fine. The perimeter that we're looking at, whether gonna put moulding now, this will have molding because it's underneath the window, right? This will not have molding because it's the door. So we want to do the perimeter. It's already did the p you fix it, it's gonna be twice the length. Plus the width 103 Premier is gonna be twice 14 was 13. But then we're gonna subtract for because we're not gonna put molding where the door is. Other is molding underneath the window, so we're going to have twice. 27 minus four. Which means twice, Twice. Oh, sorry. I thought none of it was wrong for about there. Which makes it 54. He wants attract the hour. So we need 50 feet of molding, but they only come in eight fit sections. So if I do 68 foot sections, that's 48 so I can't do that. So I got do seven sections, and I'm gonna have some left over. So $4 from seven equals 28. So there you go. $28.

So what we want to do first is to find it total area of Dez trapezoid and then multiplied by the cost per square foot. So starting off, we know the area is gonna equal 1/2 times the height, times the sum of the basis. And in this case, it's gonna be 1/2 times eight times 20 plus 12 on this is four times 32 on this gives me 120 where Just Murphy. Now we know the cost per square feet, and so the total cost is therefore going to be as your appointed You're bi. That so much the unit cost is and the total area I have is 120. So these two cans alone and in the end, you have $6.4. So that's how much the total cost us


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