OptiCraft Furniture Production Problem Maya, Ethan, and Zoe…
OptiCraft Furniture Production Problem Maya, Ethan, and Zoe are partners in a small business that designs and sells custom handcrafted furniture. Each week, Maya and Ethan are available to work up to 40 hours, while Zoe can work up to 25 hours. The company produces two main types of furniture: dining tables and coffee tables. Maya is the designer, Ethan is the woodworker, and Zoe handles sales and logistics. The time (in hours) each partner must contribute to complete one unit of each product is shown below: Dining Table Coffee Table Time Available (hrs) Design (Maya) 4 6 40 Woodworking (Ethan) 8 4 40 Sales/Logistics (Zoe) 3 2 25 Each dining table sold yields a profit of $400, and each coffee table yields a profit of $220. Determine how many dining tables and coffee tables OptiCraft should produce each week to maximize total profit, subject to labor availability constraints for each partner. What is the maximized profit under the current conditions? $[maxprofit] If Maya can work up to 10 hours of overtime, what is the highest wage per hour the company should be willing to pay for her overtime? $[overwage]/hr If Zoe can also work up to 10 hours of overtime, what is the highest wage per hour the company should be willing to pay for her overtime? $[zoeover]/hr
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