Question

A company produces remote-controlled helicopters. The company’s profit, in thousands of dollars, as a function of the number of helicopters produced per week can be modeled by a quadratic function. When 1 helicopter is produced per week, the company’s profit is 4 thousand dollars. The maximum profit, 22 thousand dollars, occurs when 4 helicopters are produced per week.
The function that models the scenario, where h is the number of helicopters produced per week, is
f(h) = –2(h – 4)2 + 22.
When 6 helicopters are produced weekly, the company’s profit is _____________
thousand dollars.

Answer 1

Answer:

When 6 helicopters are produced weekly, the company's profit is 14 thousand dollars.

Step-by-step explanation:

As per the given statement:

The company profit (in thousands of dollars), as a function of the number of helicopters produced per week can be modeled by a  function.

The function that models the scenario is:

$f(h) = -2(h-4)^2 +22$                       ......[1]

where

f(h) represents the company's profit

h represents the number of helicopters produced per week.

It is also given that when 1 helicopter is produced per week, the company’s profit is 4 thousand dollars.

Maximum profit for company 22 thousand dollars, occurs when 4 helicopters are produced per week

⇒$f(1) = 4$ and $f(4) = 22$

we have to find when 6 helicopters are produced weekly, the company profit is;

⇒  h = 6 helicopters

Substitute this value in [1] to solve for f(6);

$f(6) = -2(6-4)^2 +22$

=$-2(2)^2 +22 = -2 \times 4 + 22 = -8 + 22 = 14$

Therefore, the company profit is, 14 thousand dollars.

Answer 2

We simply substitute 6 into the equation:
f(6) = -2(6 - 4)² + 22
f(6) = 14

The company's profit is 14 thousand dollars.