Seasons Greetings (SG) manufacturers artificial holiday trees decorated with embedded multi-colored lights suitable for homes or stores, tree sales vary seasonally, with 1 thousand demanded in the first quarter of the year, 5 thousand in the second, 10 thousand in the third, and 7 thousand in the fourth. Corresponding profits to the company also vary with $50 per tree gained on sales in the high-demand third and fourth quarters, and $35 per tree in slower-demand first and second quarters. Still, SG can manufacture only 5 thousand in any quarter due to the limits of its production facility, so not all demand can be met. Inventory can be produced and held to exploit varying profit levels, but holding costs SG $12 per quarter per tree.

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

(b) Formulate a linear program to compute an optimal (max net income) sales and inventory plan for SG using the parameters of part

(a) and assuming perpetual inventory.

Use decision variables sq = sales in quarter q and hq = units held in quarter q, for q = 1,c, 4. Be sure to briefly annotate the objective function and constraints

(both main and variable-type) to indicate their meaning.

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