Arectangle 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.

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

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

step-by-step explanation:

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