Answer to Question #136455 in Calculus for Gab

Question #136455

A rectangular open box is have a square base, and its volume is to be 125 inches^3. The cost Per in^2 Of the material for the bottom Is 8$ and for the sides is 4$.


A. Find the mathematical model Expressing The total cost Of the material As a function of the edge Lenght Of the square base.


B. What is the total cost If the square Base has edge Lenght of 4 inches


1
Expert's answer
2020-10-03T15:42:42-0400

A. Denote length of the side of the square base by x.x. The volume VV of a rectangular box is equal to x2hx^2h, where hh is the heigth of the box. Therefore, h=Vx2=125x2h=\frac{V}{x^2}=\frac{125}{x^2}. The area of the lateral sides is equal to 4125x2x=500x4\frac{125}{x^2}x=\frac{500}x. Thus, the mathematical model expressing the total cost of the material can be written in the following form:

m(x)=8x2+4500x=8x2+2000xm(x)=8x^2+4\frac{500}{x}=8x^2+\frac{2000}{x}


B. If the square base has edge length of x=4x=4 inches, then its total cost is


m(4)=842+20004=128+500=628.m(4)=8\cdot 4^2+\frac{2000}{4}=128+500=628.

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