Sal's Sunglass Hut Consider the following sensitivity report for Sal's Sunglass Hut, which makes two models of sunglasses (deluxe and standard). Sal has scheduled 300 labor hours for his shipping department, 120 labor hours for production, and 20 hours for quality control. The following solution is based on maximizing profit. Name D (Deluxe S (Standard) Final Value 450 Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease 0 50 1.00E+30 7.5 0 25 10 3.5 800 Name Shipping Production Quality control Final Value 260 120 20 Shadow Constraint Allowable Allowable Price R.H. Side Increase Decrease 0 300 1.00E+30 53..5 1.5 120 32 40 -2.6 20 10 4.2 Ace, LLC Ace, LLC, manufactures two models of snowboard bindings for backcountry use. Their manufacturing plant runs three different production lines: manufacturing (M), assembly (A) and inspection and packaging (P). Their CarvePlus model requires 2.2 hours of manufacturing time, 1.5 hours of assembly time, 0.5 hours of inspection and packaging time, and makes a $60 per unit contribution to profit. Ace's VerticalDrop model requires 15% more manufacturing time, 20% more assembly time, the same 0.5 hours for inspection and packaging, and makes a $75 per unit contribution to profit. Ace estimates that they have 400 man-hours available for manufacturing, 240 man-hours available for assembly, and 100 man-hours for inspection and packaging for the coming month. They can schedule up to an additional 80 hours of (combined) overtime for their manufacturing and assembly lines at a cost of $15 per hour, but cannot use overtime for inspection and packaging. Further, Ace believes that at least 40% of the models produced must be their Carve Plus model. Acme Industries Acme Industries distributes two components, widgets and gizmos for the cell phone industry. Acme can manufacture or purchase these components at the costs listed in the table below. Clearly, it is always cheaper for Acme to manufacture the components, but Acme may not have the capacity to satisfy their demand. If they decide to manufacture, each widget requires 2 minutes of assembly time, and 3 minutes of testing time. Each gizmo requires 2.5 minutes of assembly and 4 minutes of testing. Purchased items are not subject to assembly and testing constraints. Acme estimates that they have 200 hours of assembly time and 250 hours of testing time available. Formulate a linear program that helps Acme decide how many units of widgets and gizmos they should manufacture and purchase if they had to satisfy demand of 8000 widgets and 7000 gizmos. Their objective is to minimize their total cost. Source Manufacture Purchase Widget $ 4.50 $ 5.25 Gizmo $ 6.00 $ 7.00 Problem F Consider the following constraints in a linear programming problem: 3A + 5B > 15 6A + 8B