Question

The cost to build an amusement park ride by a certain contractor is represented by the function: Cost = 2*x2 – 10/x + 36*y + 25 where x is the number of people able to be on the ride at once. For what value of x would unit cost be minimized? What is the minimum cost for this number of passengers? Show mathematically that the value found is truly a minimum and discuss whether this solution is feasible.

Answer 1

The minimum cost for this number of passengers is Rs.36.05

Explanation:

The cost to build an amusement park ride by a certain contractor is represented by the function:

`Cost = 2x^2 - (10)/(x)+ 36y + 25`

x : Number of people able to be on the ride at once.

Differentiate the function w.r.t x

`(\partial cost)/(\partial x)=4x-((-10)/(x^2))=0`

`x^3=(-5)/(2)`

x=-1.3572

Differentiate the function w.r.t y

`(\partial cost)/(\partial y)=36=0`

Minimum cost =
`2x^2 - (10)/(x)+ 36y + 25`

Minimum cost =
`2(-1.3572)^2 - (10)/((-1.3572))+ 36(0) + 25`

Minimum cost = 36.05

Hence the minimum cost for this number of passengers is Rs.36.05