Each year, a ski company manufactures its products in December and then sells them from January through March. A director informs you that this year they designed three models: Luna, Teddy, and Meowzer. The fixed cost of producing each model is $15,000. He is unsure whether to limit production to just one or two of the models instead of producing all three and incurring $45,000 in fixed costs.

The market research found that there is enough demand to support sales of 500 Luna units, 200 Teddy units, and 90 Meowzer units; the unit profit margins are $100, $300, and $700, respectively. However, it takes significant sales effort to sell skis, especially high-priced ones. He estimates that it takes 0.5 hr, 1 hr, and 3 hr of sales effort to sell 1 unit of each design, respectively. A worker has 480 hours available to sell skis during the sales season. The sky company uses a contract manufacturer for all production, and their contract gives them access to 500 hours of production capacity in December. Because of varying complexity across models, the unit production times vary in accordance: 1 hr, 1.5 hr, and 2 hr for Luna, Teddy, and Meowzer models, respectively.

(i) Determine a working optimization model that generates the optimal plan without intervention. Additionally, the director is uncertain about the unit profit margin on model Teddy. He believes there is a chance it could turn out to be lower because of the mid-range model promotions that the company typically runs. Advise him of the extent to which this unit profit margin of $300 can decrease before it leads to a change in your recommendation.