The production cost (£C) ofa bicycle in a factory is given by the function C=2x^2-200x+5100, where x is the number of bicycles manufactured per day, find the number of bicycles manufactured per day such that the production cost is a minimum.
the minimum lies on the axis of symmetry
x min = -b / 2a = -(-200) / 2*2 = 50
To find the number of bicycles manufactured per day such that the production cost is a minimum, we need to find the vertex of the quadratic function C=2x^2-200x+5100.
The vertex of a quadratic function, in the form of ax^2+bx+c, can be found using the formula x = -b/2a.
In this case, a=2, b=-200, and c=5100.
Plugging these values into the formula, we have:
x = -(-200)/(2*2)
x = 200/4
x = 50
Therefore, the number of bicycles manufactured per day such that the production cost is a minimum is 50.