Welolington is buiding a shed with a square base measuring x feet by x feet, and which is h feet high. He wants the volume of the shed to be 224 ft3. Concrete for the base costs $3 per ft2. The materials for each of the four sides cost $2 per ft2. The flat roof will cost $11 per ft2. If Wellington wants to minimize cost, the the objective function in terms of x and h is: C = . The constraint equation in terms of x and h is: 224 = . The dimensions which minimize cost are x = ft and h = ft. The minimal cost to build the shed is $

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Welolington is buiding a shed with a square base measuring x feet by x feet, and which is h feet high. He wants the volume of the shed to be 224 ft3. Concrete for the base costs $3 per ft2. The materials for each of the four sides cost $2 per ft2. The flat roof will cost $11 per ft2. If Wellington wants to minimize cost, the the objective function in terms of x and h is: C = . The constraint equation in terms of x and h is: 224 = . The dimensions which minimize cost are x = ft and h = ft. The minimal cost to build the shed is $

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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224 =x^2 h and C = 3x^2 +2*4x *h +11x^2=14x^2 +8xh=14x^2 +8x *(224/X^2) C=14x^2 +1792/x for max or min dC/dx=0 or 28x- 1792/x^2 =0 or 28x^3-1792=0 or x^3 =224
sorry for my wrong calculation as 28x^3-1792=0 or x^3 -64 =0 or x^3=4^3 hence x=4 hence at x=4 the cost may be min
for checking we have d/dx(dC/dx) = 28 +2(1792/x^3) and at x=4 d/dx(dC/dx) >0 hence at x=4 C is min when x=4 h= 224/16 =14 and C=14(16) + 1792/16 =224 + 112 =336

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oops again wrong calc for C C=14(16) +1792/4 =224 + 448 =672 (neglect 336)

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