Hello. I could really use help answering Problem 1 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 1 [50 points) TechSave Inc. is a technology company with four software development tasks and ve software engineers. Each task requires different expertise, and there are associated costs for assigning each task to a particular engineer. The objective is to minimize the total allocation costs while ensuring all tasks are allocated to skillful engineers. Your task is to formulate an optimization model that assigns each project to one engineer and minimizes the total allocation costs. Please consider that engineers cannot perform more than one task at a time, and neither Alex nor Chris will likely achieve Project Z on time. The following table provides the cost (3) for each task-engineer combination. Alex Bella Chris David Emma Project X 8 7 6 10 11 Project Y 6 Project Z 9 8 Project A 7 Questions: a) (30 points) Formulate an optimization model (decision variables, objective function, and constraints) to nd the optimal assignment that minimizes the total cost. 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