Problema Solution
A soft-drink vendor analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in pesos) is given by p(x)= -0.001x^2+3x-1800. What is the maximum profit per day and how many cans must he sell for maximum profit?
Answer provided by our tutors
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.
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The axis of symmetry is the line x = -b/(2a)
x = -3/(2*(-0.001))
x = -3/(-0.002)
x = 1500 (cans of soda)
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Profit then is:
P(x)= -0.001x^2+3x-1800
P(x)= -0.001(1500)^2+3(1500)-1800
P(x) = $4950 (maximum profit)