Example Help for Calc.

Question

A decorative box will be made. The top and bottom (base) will be square. The material needed to make the base will cost $0.20 per square foot, while the material to make the top and sides will cost $0.25 per square foot. The box must have a volume of 10 cubic feet. Minimize the cost. Let x be the width of the base in feet, and let y be the height in feet. Round your answers to 2 decimal places.

Answer 1

Let x = length of a side of the base and y = height

Then, x²y = 10. So, y = 10 / x².

C = cost = 0.20x² + 0.25(x² + 4xy) = 0.45x² + x(10 / x²) = 0.45x² + 10x^-1

dC / dx = 0.90x - 10 / x² = [0.90x³ - 10] / x²

dC/dx = 0 when 0.90x³ = 10

x³ = 11.11111

Minimum cost when x = 2.23 ft and y = 2.01 ft

Answer 2

bottom=x^2*$.2/sq/ft

sides= 4xy*$.25 "

top= x^2*$.25 "

*=10cu/ft

Need more imfo. What's the height compared to the length/width?