#1 Consider the following linear program with two decision variables, A and B. maxs.t.AAAA+2BB+B+2B12015250 Use the graphical solution method to determine the optimal solution and the associated objective function value. #2 ForeTech is a sporting equipment manufacturer that produces two different types of golf balls, the DriveMaster and the GreenHunter. The golf balls are manufactured in batches; each batch of the DriveMaster yields $10 profit, while each batch of the GreenHunter yields $6 profit. The golf balls are made using three separate processes: making the core of the ball, adding the middle layers, and coating with a synthetic resin. There is one machine for making the core and one for adding the middle layers; three machines are available for the coating process. Each machine can be operated for 10 hours per day. Both types of golf balls require 3 minutes per batch to make the core. Adding the middle layers takes 6 minutes per batch for the DriveMaster, but only 2 minutes per batch for the GreenHunter. The coating process takes 12 minutes per batch of DriveMaster and 9 minutes per batch of GreenHunter. Formulate a linear programming model to determine the optimal number of batches of each type of golf ball that ForeTech should produce, with the goal of maximizing profit. Solve the LP using the graphical solution method. #3 To crosstrain its data scientists on multiple programming techniques, SciConcepts plans to offer a three-day workshop on Python and a four-day workshop on SQL. The chief data scientist has requested that at least four of each type of workshop be offered during the current quarter. The consultant that provides these workshops has 42 days available during this quarter, and SciConcepts must contract with them for at least 12 workshops. The cost to SciConcepts is $500 for each Python workshop and $400 for each SQL workshop. Formulate a linear programming model that can be used to determine the cost-minimizing number of each type of workshop to offer this quarter. Solve the LP using the graphical solution method. MS 3053 (Panda) - Homework \#2 (Spring 2023)