Philip P. answered • 8d

Affordable, Experienced, and Patient Algebra Tutor

Let** x** be the number of $0.25 decreases in price. The number, N, of sandwiches sold is:

**N = 330 + 15x**

The price per sandwich, P, is:

**P = P**_{0}** - 0.25x**

where P_{0} is the full price (when x = 0). I suspect the problem tells you this number, so just fill in the value.

The Revenue, R, is the number of sandwiches sold times the price per sandwich:

**R = N·P**

Substitute in the expressions for N and P then multiply it out. You'll get a quadratic equation with a negative coefficient for the x^{2} term. This means the parabola is inverted and the vertex is the maximum revenue, so you'll need to find the coordinates of the vertex. The x value of the vertex is the number of $0.25 decreases that yields the maximum revenue and the y value is the maximum revenue. Plug the x value of the vertex into the price formula above to get the price per sandwich.