SOLUTION: 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)= -0.0

Question 202619This question is from textbook algebra and trigonometry
: 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 This question is from textbook algebra and trigonometry

Found 2 solutions by nerdybill, MathTherapy:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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 by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Based on maximum sales of 1,500 cans of soda, the vendor's maximum profit, or y = $.
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