EXPLANATION
Let's see the facts:
Revenue --> R(x) = 2sqrt (x) - 4 [x=number of items sold]
Cost --------> C(x) = 6 - sqrt (x)
The company will be profitable when the Revenue exceeds the cost.
Profitable condition: Revenue > Cost
Setting the two functions equal to each other and solving for x:
[tex]2\sqrt[]{x}-4\text{ = 6 - }\sqrt[]{x}[/tex]
Adding +sqrt(x) to both sides:
[tex]2\sqrt[]{x}+\sqrt[]{x}-4\text{ = 6 }[/tex]
Adding +4 to both sides:
[tex]2\sqrt[]{x}+\sqrt[]{x}\text{ = 6 }+4[/tex]
Adding similar terms and simplifying:
[tex]3\sqrt[]{x}=10[/tex]
Dividing both sides by 3:
[tex]\sqrt[]{x}=10/3[/tex]
Applying the power of 2 to both sides:
[tex]x=(10/3)^2[/tex]
Simplifying:
x=11.11
The answer is about 111. In order for a company to be profitable, their revenue must exceed their cost. Setting the two functions equal to each other and solving for x gives the minimum number of items that need to be sold in order to be profitable. OPTION B.
