A restaurant sells 330 sandwiches each day. For each $0.25 decrease in price, the restaurant sells about 15 more sandwiches.

Question

I need to know the cost of each sandwich and the max. daily revenue

Answer 1

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 = P₀ - 0.25x

where P₀ 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 x² 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.