A speculator operates a silo with a capacity of 5,000 bushels for storing corn. At the beginning of month 1, the silo contains 2,000 bushels. Estimates of the selling and purchase prices of corn during the next four months are given in the figure below. Selling and Purchase Price Data Purchase Price per 1000 Bushels (S) 40 50 70 70 Month 1 2 3 4 Selling Price per 1000 Bushels (S) 35 50 60 70 Corn sold during any given months is removed from the silo at the beginning of that month. Thus, 2,000 bushels are available for sale in month 1. Corn bought during any given month is put into the silo during the middle of that month, but it cannot be sold until the following month. Given the above sales and purchase prices, and the assumptions on storage costs presented in part a, the speculator wishes to know how much com to buy and sell each month so as to maximize total profits shortly after the beginning of the fourth month (which means after any sale that may occur in that month). To aid in defining the assumptions on storage cost let A = bushels in the silo immediately after the quantity sold in period t is removed (t-1, 2, 3, 4) a. Assume that the storage cost in period t (t=1, 2, 3) is $0.005 (A, B)/2 Define the decision variables and formulate an LP model for this problem. B = bushels in the silo immediately after the quantity purchased in period t is out into the silo (t=1, 2,3)