A manufacturer determines that the number of drills it can sell is given by the formula $D=-4 p^{2}+160 p-305$ where $p$ is the price of drills in dollars. At what price will the manufacturer sell the maximum number of drills? a) $\$ 20$ b) $\$ 40$ c) $\$ 22$ d) $\$ 80$

Step 1 ：The number of drills sold is a quadratic function of the price. The maximum number of drills sold will occur at the vertex of the parabola represented by the quadratic function. The x-coordinate of the vertex of a parabola given by the equation \(y = ax^2 + bx + c\) is \(-\frac{b}{2a}\). In this case, \(a = -4\) and \(b = 160\), so the price that maximizes the number of drills sold is \(-\frac{160}{2(-4)}\).

Step 2 ：Substitute the values of a and b into the formula: a = -4, b = 160

Step 3 ：Calculate the price p = \(-\frac{160}{2(-4)}\) = 20.0

Step 4 ：Final Answer: The price that will maximize the number of drills sold is \(\boxed{\$20}\)