Posted by Shannon on Sunday, April 3, 2011 at 3:56pm.
A company wants to bid on an order of 20,000 square based boxes which hold 5 cubic feet. The cardboard cost is $.15 per square foot. The boxes must be reinforced with an extra layer of cheaper cardboard on the bottom ($.12 per square foot). The box is held together with tape on all four edges and one side edge. There is also one edge along the top which is taped to create a hinge. It cost $.10 per linear foot to tape edges.
1. Write a function for the cost of a box based on the length of the base.
2. Graph your cost function.
3. What should the dimensions of the box be in order to minimize the cost?
4. How much will it cost to make the 20,000 boxes?
5. If the company wants to make 15% what should they bid?

calculus  bobpursley, Sunday, April 3, 2011 at 4:11pm
Which step are you having difficulty with?Doing them in sequence should give you all you need.

calculus  Shannon, Sunday, April 3, 2011 at 4:27pm
I am having difficulty coming up with the right function. The rest should fall into place, I know.

calculus  bobpursley, Sunday, April 3, 2011 at 4:58pm
area = 2 ends + 2 sides +extra bottom+ bottom+ edge+top this assumes top,two bottoms, and four sides. I assume the four edges mentioned are the three bottom edges, and one side edge.
cost=area*cost/srea= 2*h*w*.15+ 2*h*l*.15+ l*w*.15+l*w*.12+ w*l*.15 +.10(2w+h+l+w)
simplify that into a function of l,w,h
Then volume=5=lwh and you can solve h=5/lw
check carefully the area and cost function. A sketch of the box might help. I assume the bottom was hinged on one side, taped on three sides, then tape on one height side, and finally, tape for a folding lid. Weird box.

calculus  bobpursley, Sunday, April 3, 2011 at 5:02pm
remember it is square, so w=l

calculus  Shannon, Sunday, April 3, 2011 at 9:06pm
That is what I came up with for my function. It just didn't seem to work out right when I went to solve. I will have to go back and check my math. Thank you for your help!!!
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