Question

After experimentation, a certain manufacturer determined that if x units of a particular commodity are produced per week, the marginal cost is given by 0.3x -11, where the production cost is in dollars. If the selling price of the commodity is fixed at $19 per unit, and the fixed cost is $100 per week, find the maximum profit that can be obtained.

Answer 1

for x units, the profit p(x) is
p(x) = 19x-100-c(x)
where c(x) is the cost of the units.
now,
dc/dx = .3x-11, so c(x) = 0.15x^2-11x (why no +C?)
p(x) = 19x-100-(0.15x^2-11x)
= -0.15x^2 + 30x - 100
now just find the vertex of that parabola for maximum profit.