1. A rectangular storage container with an open top is to have a volume of 20 cu
ID: 2896969 • Letter: 1
Question
1. A rectangular storage container with an open top is to have a volume of 20 cubic meters. The length of its base is twice the width. Material for the base costs 11 dollars per square meter. Material for the sides costs 4 dollars per square meter. Find the cost of materials for the cheapest such container.
Total cost =
2.A box with an open top has vertical sides, a square bottom, and a volume of 256 cubic meters. If the box has the least possible surface area, find its dimensions.
Height=
Length of base=
Explanation / Answer
1) V = 20m^3, L = 2W, Cb = $11, Cs = $4 LWH = 20, 2W^2H = 20, W^2*H = 10 Total area = LW + 2(WH) + 2(LH) Total cost = 11LW + 8(WH + LH) = 22W^2 + 8(WH + 2WH) = 22W^2 + 24WH H = 10/W^2 Total cost = 22W^2 + 24W*10/W^2 = 22W^2 + 240/W Differntiate with respect to W and equate to 0 W = 1.76m Cost = $204.51 2) L^2H = 256 H = 256/L^2 Surface area = L^2 + 4LH = L^2 + 4*L*256/L^2 = L^2 + 1024/L Differentiate with respect to L and equate to 0 L = 8m H = 256/L^2 = 256/64 = 4m
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