SOLUTION: Aki's Bicycle Designs has determined that when x 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 dollars. How many bicycles
Question 473532: Aki's Bicycle Designs has determined that when x 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 dollars. How many bicycles should the shop build to minimize the average cost per bicycle? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! c(x) = -.2x^2-.1x+9.743
graph of this equation looks like this:
since x can't be negative, then only the right side of the graph is valid (x >= 0).
it appears that this graph indicates a maximum point and not a minimum point.
that's because the coefficient of the x^2 term is negative.
you can see from this graph that the cost per bicycle starts off at a maximum point when x = 0 and then tapers down to 0 when x = somewhere between 6 and 7.
there is no minimum point.
only a maximum point.
the maximum point would be found from the equation:
x = -b/2a
in this equation, a = -.2 and b = -.1
x = -b/2a = -(-.1)/(2*(-.2) which becomes .1/-.4 which becomes -1/4.
the maximum point of this graph is when x = -.25
at that point, y would be equal to -.2*(-.25)^2-.1*(-.25)+9.743.
solving this equation gets you:
y = 9.755.
the horizontal line in the graph is at y = 9.755.
note that this is a maximum point, not a minimum point.
it looks like the problem is flawed since there is no minimum point.
it appears the more bicycles that are built, the cheaper the cost, until you get to a point where the cost per bicycle is 0.
that would be at the upper root of the quadratic equation.
you would use the quadratic formula to find the exact value of this root.
the roots of this equation are:
x = -7.23408906
x = 6.73408906
the higher root is equal to 6.73408906.
the graph shows the approximate location.
bottom line is you don't really have a minimum cost point with the equation you showed, only a maximum point.
