Question

Sound Software estimates that it will sell LaTeX: NN units of a program after spending LaTeX: aa thousands of dollars on advertising, where LaTeX: N\left(a\right)=-a^2+300a+6N ( a ) = − a 2 + 300 a + 6 when LaTeX: 0\le a\le3000 ≤ a ≤ 300. What is the maximum number of units that can be sold and how much need to be spent on advertising in order to achieve this sales goal?

Answer 1

Step-by-step explanation:

From the given information:

N(a) = -a² +300a + 6

Taking the differential of the above equation with respect to "a"

Then;

N'(a) = - 2a + 300

where;

the Critical points N'(a) = 0

-2a + 300 = 0

-2a = -300

a = -300/-2

a = 150

Now;

N(0) = -(0)² +300(0) + 6

N(150) = (-150)² +300(150) + 6 =22506

N(300) = (-300)² +300(300) + 6 = 6

∴

The max. number of the possible unit that can be sold = 22506

The amount spent on advertising to get to this goal = 150 thousand dollars