Final answer:
To determine the minimum operating cost for Jane D. Minted's computer repair shop, we calculate the vertex of the parabola represented by her cost function. The result is that repairing 11 computers will result in the lowest cost.
Step-by-step explanation:
Jane D. Minted owns and operates a computer repair shop, where the cost of operating her shop is given by the quadratic function C = 2.5x2 - 55x + 425, where C represents the cost in dollars and x represents the number of computers repaired.
To find the number of computers she must repair to have the lowest cost, we can calculate the vertex of the parabola represented by this function since the coefficient of x2 is positive, indicating a parabola that opens upwards and hence the vertex will give us the minimum point.
To find the vertex, we use the formula x = -b/(2a) where a and b are the coefficients from the quadratic equation ax2 + bx + c.
In this case, a = 2.5 and b = -55, which when plugged into the formula gives us:
x = -(-55)/(2 * 2.5)
= 55/5
= 11
Therefore, Jane must repair 11 computers to have the lowest operating cost.