Respuesta :
Answer: 2.125 million (Approx)
Step-by-step explanation:
Let the company initially produced x million hoops.
Therefore, after reducing 1 million hoops,
New number of hoops = (x-1)
Since, Profit = Sale price - Cost price
The cost price of 1 hoop = 30 dollars
Thus, the cost price of (x-1) million hoop = 30(x-1) dollars
According to the question,
The price that a company charged for a basketball hoop is given by the equation [tex]50-(x-1)^2[/tex]
Thus the sales price of x million hoops = [tex]50 - (x-1)^2[/tex]
Hence, the company's profit = [tex](50 - (x-1)^2) - 30(x-1)[/tex]
Again According to the question,
The company's profit = 15 million,
⇒ [tex](50 - (x-1)^2) - 30(x-1)=15[/tex]
⇒ [tex]50-x^2-1+2x-30x+30=15[/tex]
⇒ [tex]-x^2-28x+79-15=0[/tex]
⇒ [tex]-x^2-28x+64=0[/tex]
⇒ [tex]x^2+28x-64=0[/tex]
By solving this equations we get,
x = -2(7+√65) and x = 2(√65-7)
But, the number of hoops can not be negative,
Thus, the initial number of hoops = 2(√65-7) million =2.1245154966 million ≈2.125 million
