Answer: The correct option is first, the number of basketball hoops did the company previously produce to make the same profit is 1.3 million hoops.
Explanation:
Let the number of basketball hoops did the company previously produce to make the same profit be x.
Total Revenue = Price * Quantity
The total revenue in million dollars is,
[tex]\text{Total Revenue}=(50-5x^2)x[/tex]
[tex]\text{Total Revenue}=50x-5x^3[/tex]
The total cost in million dollars is,
Total Cost = One unit cost * Quantity
[tex]\text{Total Cost}=30x[/tex]
Profit = Total Revenue - Total Cost
[tex]\text{Profit}=50x-5x^3-30x[/tex]
The profit is 15 million.
[tex]15=20x-5x^3[/tex]
[tex]5x^3-20x+15=0\\x^2-4x+3=0\\(x-1)(x^2+x-3)=0[/tex]
The value of x is 1 and [tex]\frac{-1\pm \sqrt{13}}{2}[/tex].
The production is always positive therefore the value of x either 1 or 1.3. Since 1 million is not available in the options therefore the the correct optin is 1.3 million hoops.
