A bike design company has determined that when X hundred bicycles are built, the average cost per bike is given by C(x)=0.2x^2-1.3x+2.995,where C(x)is in hundreds of dollars. How many bikes should the shop build to minimize the average cost per bike?
Thanks....
To minimize the average cost per bike, we need to find the minimum point on the graph of the cost equation C(x) = 0.2x^2 - 1.3x + 2.995.
To find the minimum point, we need to find the x-value that corresponds to the vertex of the quadratic equation. The x-value of the vertex can be obtained using the formula x = -b / (2a), where a, b, and c are coefficients of the quadratic equation in the form ax^2 + bx + c.
Here, the quadratic equation is in the form C(x) = 0.2x^2 - 1.3x + 2.995. Comparing this with the standard form ax^2 + bx + c, we have a = 0.2, b = -1.3, and c = 2.995.
Substituting these values into the formula x = -b / (2a), we have:
x = -(-1.3) / (2 * 0.2)
x = 1.3 / 0.4
x = 3.25
Therefore, the shop should build approximately 3.25 hundred (or 325) bikes to minimize the average cost per bike.