Question

SHOW YOUR STEPS PLEASE. SOMEONE PLEASE HELP ME I NEED THE ANSWER ASAP!!!

The cost, c(x), in dollars per hour of running a certain steamboat is modelled by the function c(x)=1.7x^2-13.6+166.4, where x is the speed in kilometres per hour. At what approximate speed should the boat travel to achieve minimum cost? what is the minimum cost?​

Answer 1

x = 4

139.2

Explanation:

Given the Cost function :

C(x) = 1.7x² - 13.6x + 166.4

To achieve minimum cost ;

dc/dx = 0

dc/dx = 2(1.7)x - 13.6

3.4x - 13.6 = 0

3.4x = 13.6

x = 13.6 / 3.4

x = 4

To achieve minimum cost, speed = 4 ;

Minimum cost will be :

C(x) = 1.7x² - 13.6x + 166.4

Put x = 4

C(4) = 1.7(4)² - 13.6(4) + 166.4

C(4) = 27.2 - 54.4 + 166.4 = 139.2

Minimum cost = 139.2