At what quantity (in hundreds of subscription boxes) does the farmer achieve the maximum profit? Profit function: P⁡(x)=−(11)/(20)​x^2+4⁢x−5 The formula to find the x -coordinate of the vertex for a quadratic function a⁢x^2+b⁢x+c is x=−(b)/(2⁢a)

The profit function is a downward-opening quadratic because its leading coefficient is negative, so its vertex gives the maximum profit. Here, a = −11/20 and b = 4, so x = −b/(2a) = −4/[2(−11/20)] = 40/11. The farmer achieves maximum profit at 40/11 hundreds of subscription boxes, choice C.

AI-written and checked against the verified answer.