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1. After watching the two videos answer the following questions: a. What are the underlying assumptions when we model a business problem as a linear program? b. What is the optimal solution to the custom molder problem? That is, how many cases of 6-oz glasses and 10-oz glasses should the molder produce? (The spreadsheet GlassManufacturer_LP_Geometry in the Lecture 1 folder has the problem data) a.) Following are the assumptions taken Proportionality: The effect of the decision variable is proportional to its coefficient. Additivity: The contribution to the objective by one decision variable is not associated with the contribution by the other decision variable (contributions are independent) Divisibility: Each decision variable can take fractional values Data certainty: Coefficients for decision variables are constant, they are not random variables. b.) The values of X1 and X2 are as mentioned below. VARS PROFIT X1 6.43 500 X2 4.29 450 Z C1 C2 C3 6 10 1 5 20 0 60.000 150.000 6.429 <= <= <= 60 150 8 N1 N2 -1 0 0 -1 -6.429 -4.286 <= <= 0 0 5142.86 c.) Consider the following feasible region to a linear programming problem, which is represented by the grey shaded area. Which of the following can possibly be a unique optimal solution (optimal for some objective function)? The candidate solution point is the red dot. Answer Yes/No to each part. i. NO ii. NO iii. YES iv. YES v. NO