What is the largest possible profit the producers can make in 1 day?

Question

Maximizing Profits

 The management of the producers of a famous hot sauce estimate that their profit (in dollars) from the daily production and sale of x cases (each case consisting of 24 bottles) of the hot sauce is given by

P(x) = −0.000003x³ + 9x − 200

Answer 1

The maximum profit is where the derivative is zero.

The derivative is -0.000009x²+9

9=0.000009x² gives two values for x, namely ±1000. We can obviously toss out the negative, as you can do in many real-world problems.

The profit is -0.000003(1000)³+9(1000)-200 = -3000+9000-200 = 5800 ■