Suppose that the decision variables of a mathematical programming model are xi, j, t! acres of land plot i allocated to crop j in year t where i = 1,c, 47; j = 1,c, 9; t = 1,c, 10.

Use summation and “for all” indexed notation to write expressions for each of the following systems of constraints in terms of these decision variables, and determine how many constraints belong to each system.

(a) The total acres allocated in each year to each plot i cannot exceed the available acres there

(call it pi).

(b) At least 25% of the total acreage allocated in each of the first 5 years years should be devoted to corn (crop j = 4).

(c) More acres should be devoted to beans (crop j = 1) in each year and each plot than to any other crop.