The price that a company charged for a basketball hoop is given by the equation 50 minus 5 x squared where x is the number of hoops that are produced, in millions. It costs the company 30 dollars to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?

At the new production level of 1 million hoops, the price is $50 − 5(1)² = $45 per hoop. After the $30 production cost, the profit is $15 per hoop, or $15 million total. For production of x million hoops, set total profit equal to 15 million: x(50 − 5x² − 30) = 15. Solving gives the other positive production level x = (−1 + √13)/2 ≈ 1.3 million hoops, so the answer is 1.3 million hoops.

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