Goings Engine produces diesel engines and assemblies i = 1,c, m at its plants p = 1,c, n.

There is some end demand di, p for the various engines and assemblies, with the rest used in Goings production. The number of subassemblies i required to produce each assembly k is ai, k.

(a) Write a system of linear constraints specifying that the number of each engine and assembly must balance (with zero inventories)

across the company using the parameters above and the nonnegative decision variable xi, p ! number of assemblies i produced at plant p.

(b) Write a system of linear constraints specifying that the number of each engine and assembly must balance (with zero inventories)

at each plant using the foregoing parameters and the nonnegative decision variable xi, p, q ! number of assemblies i produced at plant p for use at plant q.