The corn yield on a certain farm is Y = −0.118x² + 8.5x + 12.9 (bushels per acre) where x is the number of corn plants per acre (in thousands). Assume that corn seed costs $1.25 (per thousand seeds) and that corn can be sold for $1.50/bushel. Let P(x) be the profit (revenue minus the cost of seeds) at planting level x.
(a) Compute P(x₀) for the value x₀ that maximizes yield Y.
(b) Find the maximum value of P(x). Does maximum yield lead to maximum profit?