know how many containers of each product to prepare in order to maximize profit. Cost per ounce for apple juice is .2$, for grape juice [1.0433, and for Cranberry juice 0.3$. All products are sold in 64 on. containers. The applecranberry juice is also sold in a one quart size. The company has an order for It] containers of apple juice and 12 containers of the applecranberry one-quart size that must he tilled from current supplies. Formulate linear programming model of this problem. Back Savers is a company that produces backpacks primarily for students. They are considering offering some combination of two different modelsthe Collegiate and the Mini. Both are made out of the same ripresistant nylon fabric. Back Savers has a long term contract with a supplier of the nylon and receives a SJJIJIIIsquarefoot shipment of the material each week. Each Collegiate requires 3 square feet while each Mini requires 2 square feet. The sales forecasts indicate that at most 1,0{10 Collegiates and 1200' Minis can be sold per week. Each Collegiate requires 45 minutes of labor to produce and generates a unit prot of $32. Each Mini requires all] minutes of labor and generates a unit prot of $24. Back Savers has 35 laborers that each provides 4i] hours of labor per week. Management wishes to know what quantity of each type of backpack to produce per week. a.Formulate and solve a linear programming model for this problem. b. Use the graphical method to solve this model. c.3olve for Slack Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the HydroLuz. 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. {This 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 Elli] 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 AquaSpa requires 9 hours of labor and 12 feet of tubing. Each HydroLust requires 5 hours of labor and 16 feet of tubing. Howie expects