Chapter 6.5, Problem 39E

Business: minimizing costs with constraints. Farmer Frank grows two crops: celery and lettuce. He has determined that the cost of planting these crops is modeled by

$C\left(x,y\right)=x^2+3xy+3.5y^2-775x-1600y+250,000,$ where x is the number of acres of celery and y is the number of acres of lettuce. Suppose Farmer Frank has 300 acres available for planting and must plant more acres of lettuce than of celery. Find the number of acres of celery and of lettuce he should plant to minimize the cost, and state the cost.