the total cost of producing a type of truck is given by ( c(x) = 23000 - 60x + 0.05x^{2} ), where ( x ) is…

the total cost of producing a type of truck is given by ( c(x) = 23000 - 60x + 0.05x^{2} ), where ( x ) is the number of trucks produced. how many trucks should be produced to incur minimum cost? answer/how to enter your answer (opens in new window) 2 points keyboard keyboard shortcuts trucks

the total cost of producing a type of truck is given by ( c(x) = 23000 - 60x + 0.05x^{2} ), where ( x ) is the number of trucks produced. how many trucks should be produced to incur minimum cost? answer/how to enter your answer (opens in new window) 2 points keyboard keyboard shortcuts trucks

Answer

Explanation:

Step1: Find the derivative of the cost function

The cost function is ( C(x) = 23000-60x + 0.05x^{2}). Using the power rule ((x^{n})^\prime=nx^{n - 1}), the derivative (C^\prime(x)=-60 + 0.1x).

Step2: Set the derivative equal to zero

To find the critical points, set (C^\prime(x)=0). So, (-60+0.1x = 0).

Step3: Solve for (x)

Add (60) to both sides: (0.1x=60). Divide both sides by (0.1): (x=\frac{60}{0.1}=600).

Step4: Check the second - derivative

The second - derivative (C^{\prime\prime}(x)=0.1>0). Since the second - derivative is positive, the function (C(x)) has a minimum at (x = 600).

Answer:

(600)