An open rectangular box with a square ends having volume of 6400 cu: ft. is to be build at cost of 75 cents per sq: ft. for the base and 25 cents per sq- ft. for the sides Find the most economical dimensions Form the cost function that you need to minimize. Hint: Let C be the cost in cents. b) Use methods of calculus to determine the dimensions of the box that min- imizes your cost. c) Determine the actual cost of this least expensive box:
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Step 1
Step 1: The volume of the rectangular box is given as 6400 cu ft, which can be expressed as the product of the base area (x^2) and the height (y): x^2 * y = 6400. Show more…
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A rectangular box with volume $320 \mathrm{ft}^{3}$ is built with a square base and top. The cost is $\$ 1.50 / \mathrm{ft}^{2}$ for the bottom, $\$ 2.50 / \mathrm{ft}^{2}$ for the sides, and $\$ 1 / \mathrm{ft}^{2}$ for the top. Let $x=$ the length of the base, in feet. (FIGURE CAN NOT COPY) a) Express the cost of the box as a function of $x .$ b) Find the domain of the function. c) Graph the function with a graphing calculator. d) What dimensions minimize the cost of the box?
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