Hello. I could really use help answering Problem 2 questions a) and b) for my Intro To Management Science MGS411 Class below so I understand it for my exam coming up. I am struggling in this class and this would be a great help to me.

Problem 2 (50 points! StellarCra, a space equipment manufacturer, produces three types of space components: "Plasma Thrusters," "Navigation Systems," and "Solar Panels." StellarCra needs to determine the optimal production plan for the next month to maximize its total prot while considering constraints on production hours and metal supply. The following data has been given to solve the problem: 0 The company has a maximum of 3 ,5 00 hours of production time available, with each hour costing $7. 0 The company can acquire an unlimited metal supply, but it costs $2.2 per kilogram. o StellarCraft has a xed monthly cost of $2200 associated with warehouse rentflease. - There are minimum demand requirements for each product that StellarCraft must meet. 0 The table below presents the sale prices, the number of hours, the kilograms of metal required for each product, and the minimum demand requirements: gamma, Meagaageeag Plasma Thrusters $5900 1-5 Kg Navigation Solar Panels $1,500 0.8 Kg Your task is to build an optimization model to estimate the optimal production schedule for the next month, considering the constraints on production hours and metal supply and ensuring that the minimum demand requirements are met for each product. The goal is to maximize the total prot (revenue minus costs), including sales revenue and the associated production and metal costs. Questions: a) (30 points) Formulate an optimization model (decision variables, objective function, and constraints) to help the company identify the optimal production plan. b) (20 points) Solve the model using Lingo/Excel and explain your results. Lingo Model - Exercise2 Solutions Max= 12*X1 + 16*X2 + 14*x3 - 2200; 4.5*X1 + 1.8*x2 + 3. 6*X3 = 300; Exercise 1 X2 >= 550; X3 >= 320; Decision variables Xi: number of hours per week doing CrossFit, cycling, and swimming, i= 1, 2, 3. Optimal solution: Objective function The production schedule for the next month should be 300 frills, 554 seals and 320 axles to maximize profits at $14,751. Min Hours (Z) = X1 + X2 + X3 Constraints Exercise 3 C1: X2 2 X1 + X3 Decision variables C2: X3 2 2. C3: 600X, + 300X2 + 300X3 2 3000 X: number of gallons of regular gasoline, premium gasoline and Diesel, i= 1, 2, 3, to produce. Lingo model: Yj: number of gallons of crude and refined oil to use in the production process j=1, 2 Objective function Lingo Model - Exercisel DO X Min= x1 + x2 + x3; Max (Z) 4X1 + 4.5X2 + 4.1X3 - (3Y, + 3.512) x2>= x1+x3; Constraints x2-x1-x3>=0; x3>=2; C1: Y1 = 0. 4X1 + 0.30X2 + 0.50X3 600*x1+ 300*x2+ 300*x3>=3000; C2: Y2 = 0.6X1 + 0.7X2 + 0.50X3 C3: Y, S 5000 Optimal solution: C4: Y2 S 7000 The person should spend 2 hours on CrossFit, 4 hours cycling, and 2 hours swimming. The minimum number of hours Lingo model: exercising per week is 8. Max = 1*X1 + 4.5*x2 + 4. 1*x3 - (3*Yl + 3.5*Y2) ; Exercise 2 . 3*X2.10.5*X3; Y1 - 0. 4*X110 . 3*X (2 - 0. 6*X1+0 . 7*X2+0.5*X3; Decision variables Y1