Operations Management: production cycle

83. Hot Tubs: Quantity Discount. Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys prefabricated fiberglass hot tub shells from a local supplier and adds the pump and tubing to the shells to create his hot tubs. (The supplier has the capacity to deliver as many hot tub shells as Howie needs.) Howie installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labor required. Each Aqua-Spa requires 9 hours of labor and 12 feet of tubing. Each Hydro-Lux requires 11 hours of labor and 16 feet of tubing. Howie expects to have 1,520 production hours and 2,650 feet of tubing available during the next production cycle. Howie earns a profit of $350 on each Aqua-Spa he sells and $300 on each Hydro-Lux he sells. If Blue Ridge Hot Tubs produces more than 75 Aqua-Spas, it obtains discounts that increase the unit profit to $375 for all units. If it produces more than 50 Hydro-Luxes, the profit increases to $325 for all units.
His marketing team tells him that he can sell at most 150 Aqua-Spas and 100 Hydro-Luxes. How many of each should Howie produce if he wants to maximize his profits during the next production cycle?

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