Suppose a farmer has 40 acres of land to allocate each year between the production of corn and the production of wheat.Let C denote acres planted in corn and let W denote acres planted in wheat.He can sell the output from one acre planted in corn for $60 and the output from one acre planted in wheat for $70.The total (not per acre) cost of the variable inputs for corn production is C² while the total cost for wheat production is 2W².

(a) Find the number of acres the farmer will plant in corn and the number he will plant in wheat if he seeks to maximize total profit.

(b)What is the optimal value of the Lagrangian multiplier for this problem?What is its interpretation?

(c)Suppose the farmer's neighbor offers to lease to him an additional acre of land for $20 per year.Without resolving the farmer's problem, determine whether the farmer should accept or reject the offer.