Question

SALES: A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sales x cans of soda pop in one day , his profit (in dollars) is given by P(x)= -0.001x^2+3x-1800

Answer 1

You don't state what the question is -- But, I assume they want you to find the MAXIMUM profit. . Looking at: P(x)= -0.001x^2+3x-1800 Since it is a quadratic, we know it is in the shape of a parabola. The coefficient associated with the x^2 term will tell you whether it is concave up or concave down. Since it is negative (think sad face) it is concave down. Once we know that, all we have to do to find the max is to find the vertex. . The axis of symmetry is the line x = -b/(2a) x = -3/(2*(-0.001)) x = -3/(-0.002) x = 1500 (cans of soda) . Profit then is: P(x)= -0.001x^2+3x-1800 P(x)= -0.001(1500)^2+3(1500)-1800 P(x) = $4950 (maximum profit) . Vertex is at (1500, 4950)

Answer 2

Based on maximum sales of 1,500 cans of soda, the vendor's maximum profit, or y = ${{{highlight(450)}}}.