Ace Green Windows (AGW) manufactures environmentally efficient windows as replacements of those in existing homes. It has just received a contract for the next 6 months, requiring 100, 250, 190, 140, 220, and 110 units in months 1 through 6, respectively. Production costs for windows vary with time due to the specialized materials.

AGW estimates production will cost $250,

$450, $350, $400, $520, and $500 per unit in periods 1 through 6, respectively. To take advantage of cost variations, AGW may produce more windows than the contract requires in some months and hold up to 375 of them in inventory for later months. But holding inventory costs $30 per window per month.

Assume there is no beginning inventory.

(a) Define symbolic parameters naming and indexing the constants described above.

(b) Formulate a time-phased linear program to compute an optimal (minimum total cost) finite-horizon, manufacturing and inventory plan for the next 6 months using the parameters of part (a). Use decision variables xt = units produced in month t and ht = units held in month t, for t = 1,c, 6. Briefly annotate the objective function and constraints (main and variable-type) with a few words indicating their meaning.

(c) Enter and solve your model with class optimization software.