Ask Question
24 May, 16:57

A rectangle warehouse will have 5000 square feet of floor space and will be separated into two rectangular rooms by an interior wall. The cost of the exterior walls is $150 per linear foot and the cost of the interior wall is $100 per linear foot. Find the dimensions that will minimize the cost of building the warehouse.

+3
Answers (1)
  1. 24 May, 19:43
    0
    x = 59.4 ft

    y = 84.18ft

    Step-by-step explanation:

    The cost of exterior walls is $150 per linear foot.

    The cost of interior walls is $100 per linear foot.

    xy = 5000

    y = 5000/x

    For the exterior walls, we have 2 (x+y) (120)

    For the interior wall, we have 100x

    The cost function = C

    C = 2 (x+y) (120) + 100x

    C = 240 (x+y) + 100x

    = 240x + 240y + 100x

    = 340x + 240y

    Recall that y = 5000/x

    C = 340x + 240 (5000/x)

    C = 340x + 1200000/x

    Differentiate C with respect to x

    C' (x) = 340 - 1200000/x^2

    = (340x^2 - 1200000) / x^2

    To minimize cost C' (x) = 0

    (340x^2 - 1200000) / x^2 = 0

    340x^2 - 1200000 = 0

    340x^2 = 1200000

    x^2 = 1200000/340

    x = √1200000/340

    x = 59.4 ft

    Recall that y = 5000/x

    y = 5000/59.4

    y = 84.18 ft
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A rectangle warehouse will have 5000 square feet of floor space and will be separated into two rectangular rooms by an interior wall. The ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers