An economist hired by a company that makes a popular line of indoor grills predicts that consumers in one market will buy $x$ units per week if the price is $p=-0.29 x+59$ dollars. The profit is given by the equation
\[
P=-0.12 x^{2}+41 x-560
\]
Part: 0 / 2
Part 1 of 2
Use the graph to estimate the number of indoor grills they'd need to sell to make the largest possible profit. Round your answer to the nearest ten.

Step 1 ：The profit function is a quadratic function. The maximum value of a quadratic function is at its vertex. The x-coordinate of the vertex of a quadratic function given in the form \(f(x) = ax^2 + bx + c\) is \(-b/2a\).

Step 2 ：In this case, \(a = -0.12\) and \(b = 41\), so the number of grills they'd need to sell to make the largest possible profit is \(-41/(2*-0.12)\).

Step 3 ：Calculate this value and round it to the nearest ten.

Step 4 ：The calculation gives us an x value of approximately 170.83333333333334.

Step 5 ：Rounding this to the nearest ten gives us 170.

Step 6 ：Final Answer: The company needs to sell approximately \(\boxed{170}\) indoor grills to make the largest possible profit.