A local company manufactures netbook computers. Their profit function is given by this equation: y equal minus x to the power of 2 plus 100 x plus 4000 where x is the number of netbooks produced in one day and y is the profit (in dollars) the company makes that day. What is the maximum profit that the company can make?

Question

Mathematics

Briana Watkins

6 December, 10:57

A local company manufactures netbook computers. Their profit function is given by this equation: y equal minus x to the power of 2 plus 100 x plus 4000 where x is the number of netbooks produced in one day and y is the profit (in dollars) the company makes that day. What is the maximum profit that the company can make?

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Philip Ramsey · Answer 1

The equation described above can also be written as,

y = - x² + 100x + 4000

To get the number of notebooks that will give them the maximum profit, we derive the equation and equate to zero.

dy/dx = - 2x + 100 = 0

The value of x from the equation is 50. Then, we substitute 50 to the original equation to get the profit.

y = - (50^2) + 100 (50) + 4000 = 6500

Thus, the maximum profit that the company makes is $6,500/day.