Optimization Problem, Please, I Need Help By Tomorrow, Can Anyone Please Help Me?

Question

I have 3 questions.

The volume of a rectangular box is 16m^3. The box has a square base and top. The material for the base costs $7.25/m^2, for the top costs $2.25/m^2, and for the sides coss $4.25/m^2. For practical reasons, no dimension may be less than 1m. Determine the dimensions that will minimize the cost of the materials for the box. Show all your calculations and include a labelled diagram.
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A man is at point A on a bank of a straight river, 3km wide, and wants to reach point B, 8km downstream, on the opposite bank. He could row his boat directly across the river to point C and then run to B, or he could row directly to B, or he could row to some point D between C and B and then run to B. If he can row at 6km/h and run at 8km/h, how far from B should he land t reach B as soon as possible? Show all your calculations.
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A Norman window is made up of a semicircle and a rectangle. The total perimeter of the window is 32m. Determine max area of window. Show calculations.

Answer 1

I can knock off the first two easily enough.
1. You've already set the price for the top and bottom no matter how big they are. So to minimize the cost of the sides you want them to be as small as possible( letting the top and bottom make up the difference in the volume ). Since 1m is the minimum allowed the box would be 4*4*1 or 16*1*1 or some other combination where the bottom area is 16 and the sides are 1m.

2. First determine the hypotunuse of triangle abc
8^2 + 3^2 = h^2
64+9=h^2
73=h^2
h=8.54 approx
If he rowed straight across the river that'd take half an hour , plus another hour to run downstream would make that trip 90 minutes. Rowing straight from a to b would take approximatly 85 minutes. That'd be the shortest amount of time possible.

For 3 use the formula x + 3.14x/2 +2y -32 =0 where x the width and y is the height
now pick #s to use for x and solve for y
Then substitute those numbers into the equasion for the area of the shape x * y + 3.14(x/2)^2 and find the smallest one.

Answer 2

1) Box could be 1X1X16 or 2X2X4 or 4X4X1. first one costs $281.50. second one costs $310. third one costs $169.
2) A to C takes 0.5hr, C to B takes 1.3 hr. A to B is 8.54 km and takes 1.4 hr.
A to a pt halfway between C and B called D...A to D is 5km and takes 0.83 hr and D to B is 4km and takes 0.5, which is total of 1.33.
A to a pt 2km from C on land is called E...A to E is 3.6km and takes 0.6 hr, E to B is 6 Km and takes 0.75hr, total of 1.35.
A to a pt 6 Km from C is called F ...A to F is 6.7km and takes 1.1 hr, F to B is 2km and takes0.25 hr, total of 1.35
3).I get 2.57 D (diameter) plus 2 y equals 32 m. I give up.