A toy manufacturer determines that the daily cost,C, for producing x units of a dump truck can b approximated by the function c(x)=0.005x^2-x+109
I got that the manufacturer must produce 100 units per day...
What is the minimum daily cost?
put in 100 for x, and calculate c(100)
To find the minimum daily cost, we need to determine the value of x that minimizes the cost function c(x)=0.005x^2-x+109. This can be done by finding the vertex of the quadratic function.
The vertex of a quadratic function in the form ax^2+bx+c is given by the formula x = -b/2a. In this case, a = 0.005 and b = -1.
Substituting the values of a and b into the formula, we have x = -(-1)/(2*0.005) = 1/(0.01) = 100.
So, the minimum cost is achieved when the manufacturer produces 100 units per day.
To find the minimum daily cost, we need to substitute the value of x back into the cost function:
c(100) = 0.005(100)^2 - 100 + 109
= 0.005(10000) - 100 + 109
= 50 - 100 + 109
= 59.
Therefore, the minimum daily cost for producing 100 units of a dump truck is $59.
To find the minimum daily cost, we need to find the value of x that minimizes the cost function c(x) = 0.005x^2 - x + 109.
To do this, we can use calculus, specifically the concept of the derivative. We take the derivative of the cost function with respect to x and set it equal to zero:
c'(x) = 0.01x - 1 = 0
Solving for x, we get:
0.01x = 1
x = 100
So, the minimum daily cost occurs when the manufacturer produces 100 units per day.
To find the minimum daily cost, we substitute this value of x into the cost function:
c(100) = 0.005(100)^2 - 100 + 109
= 0.005(10000) - 100 + 109
= 50 - 100 + 109
= 59
Therefore, the minimum daily cost is 59.