Albert cornman makes his living buying and selling corn. on january 1 he has 50 tons of corn and $15,000 cash in his bank account. the bank pays an interest of 0.5% per month for the money in albert’s account. on the first day of each month albert can buy corn at the following prices per ton: jan $300, feb $350, mar $350, apr $500, may $500, jun $500. on the last day of each month he can sell corn at the following prices per ton: jan $250, feb $400, mar $350, apr $550, may $550, jun $600. albert stores his corn in a warehouse that can hold at most 100 tons of corn. the lease on the warehouse expires at the end of june; hence he must sell all of his corn by the end of june. each month corn loses 4% of its weight; that is, for instance, 50 tons of corn he owns on jan 1, weighs 0.96 * 50 = 48 tons on the last day of jan (and on the first day of feb, for the purpose of modeling). albert must pay cash for all corn at the time of purchase.(a) write a linear programming model to maximize albert cornman’s cash on hand at the end of june. define the decision variables clearly. explain the objective and constraints. b) solve part (a) in ampl. what is the optimal solution and the optimal objective value? print and attached your ampl code.(c) now on the first day of each month before buying corn, albert can borrow money from the bank at an interest rate of 1% per month. the total loan amount he carries cannot exceed 50% of the value of his corn, priced at $300 per ton for the purposes of loan by the bank. all loans must be paid back at or before the end of june. revise your formulation to model this new scenario.