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

Answer:

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

Step-by-step explanation:

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

$Cost = 2x^2 - \frac{10}{x}+ 36y + 25$

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

Differentiate the function w.r.t x

$\frac{\partial cost}{\partial x}=4x-(\frac{-10}{x^2})=0$

$x^3=\frac{-5}{2}$

x=-1.3572

Differentiate the function w.r.t y

$\frac{\partial cost}{\partial y}=36=0$

Minimum cost =$2x^2 - \frac{10}{x}+ 36y + 25$

Minimum cost = $2(-1.3572)^2 - \frac{10}{(-1.3572)}+ 36(0) + 25$

Minimum cost = 36.05

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