Aki’s Bicycle has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=-0.2x^2-0.1x+9.743, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle? They should build? bicycles
With minus signs in front of both of the first two terms, the average cost keeps decreasing with increasing x.
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To find the number of bicycles that Aki's Bicycle should build to minimize the average cost per bicycle, we need to find the value of x that corresponds to the minimum point of the function C(x).
The average cost per bicycle is given by the function C(x) = -0.2x^2 - 0.1x + 9.743. This is a quadratic function, and the x-value of the minimum point can be found using the vertex formula: x = -b / (2a), where a and b are the coefficients of the quadratic equation.
In this case, a = -0.2 and b = -0.1. Plugging these values into the vertex formula, we get:
x = -(-0.1) / (2 * -0.2)
x = 0.1 / (-0.4)
x = -0.25
The value of x is -0.25. However, since x represents the number of hundreds of bicycles, a negative value does not make sense in this context. Therefore, we can conclude that Aki's Bicycle should build 0 bicycles, or no bicycles at all.
Note: It is important to consider the assumptions and limitations of the problem when interpreting the result. In this case, it seems that the given function C(x) does not have a realistic minimum value, so it might be necessary to re-evaluate the equation or consider other factors.