Question

The equation relating the number of customized cell phones produced and the profit per cell phone is p=-2.50n2+21n, where n is in 100000s. Plot the resulting graph. Be sure to label and number the axes appropriately and indicate the maximum value of p

Answer 1

Please find attached the graph of the profit function created wit Microsoft Excel

The maximum profit, p
`_(max)` = 4,410,000

Explanation:

The given equation is presented as follows;

The profit, p = -2.5·n² + 21·n

The value of n is given in 100,000 s

Differentiating the profit function and equating the result to zero to find the values for the maximum profit, we have;

d(-2.5·n² + 21·n)/dn = -5·n + 21 = 0

n = 21/5 = 4.2

The maximum profit, f(4.2) = -2.5 × 4.2² + 21 × 4.2 = 44.1

The maximum profit, f(4.2) = 44.1 × 100,000 = 4,410,000