Question

Please help me!! I have been stuck for hours

Answer 1

The optimum price to sell the app is $2.55

Explanation:

Modeling With Functions

The equation of the demand for the app store is given by

U=10000-2000P

Where U is the number of units sold and P is the price for each unit.

a.

The money from sales (Revenue) is U times the price of each unit, so

`S=U.P`

Using the equation above

`S=(10000-2000P).P=10000P-2000P^2`

b. The upfront costs function is given by

`C=2000+0.1U`

Again, we use the equation for U

`C=2000+0.1(10000-2000P)`

`C=2000+1000-200P`

`C=3000-200P`

c.

The profit is the sales minus the cost

`Profic=S-C=10000P-2000P^2-(3000-200P)`

`Profit=10000P-2000P^2-3000+200P`

`Profit=-2000P^2+10200P-3000`

d.

The vertex of a quadratic function shown as

`f(x)=ax^2+bx+c`

has an x-coordinate equal to

`\displaystyle x=-(b)/(2a)`

The optimum price for selling the app can be found in the vertex of the above equation.

The P-coordinate of the vertex is given by

`\displaystyle x=-(10200)/(-4000)=2.55`

The optimum price to sell the app is $2.55