THE PIGSKIN BALLET SHOES The PigSkin Company produces ballet shoes for children aged 3 to 7. The shoes have three sizes: S, M, and L. Each size has its independent monthly demand, which identically follows a binary

distribution with D _ {300 with probability 0.25

5‘ _ 100 with probability 0.75 D _ {300 with probability 0.35

M _ 100 with probability 0.65 300 with probability 0.45 D“ = {100 with probability 0.55 where t = 1, 2, ..., 12. The unit production cost for the three sizes are $6, $7, and $8 per pair,

respectively. The selling prices are all 520 per pair. The company has a limited production capacity, and a maximum of 600 pairs of shoes in total

can be produced each month. Besides the capacity constraint, the budget for shoe production

is also constrained each month by the amount of cash available. At the beginning, the company has 55,000 on hand. At the end of each month, the company has to pay a total wage of $6,000. All other expenses excluding productions and wages are ignored.