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- This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows: 14, 58, 912, 1316, and 1720. a. Find the optimal investments when at most one investment from each group can be selected. b. Find the optimal investments when at least one investment from each group must be selected. (If the budget isnt large enough to permit this, increase the budget to a larger value.)Consider the following set of constraints: -4X <= -512; -28Y <= -3584; 0.5 X + 14Y >= 1792, and 2X + 2Y <= 256. Pick a right statement for this problem: a. Feasible region is represented by a line and multiple feasible points are available. b. The feasible region is defined by a single (unique) point. c. Feasible region does not exist. d. All the options are incorrect. e. Solution to this problem cannot be found without the objective function
- Consider the following linear programming model with 4 regular constraints:Maximize 3X + 5Y (a) Draw your graph in the space below:subject to: 4X + 4Y ≤ 48 (constraint #1) 4X + 3Y ≤ 50 (constraint #2) 2X + 1Y ≤ 20 (constraint #3) X ≥ 2 (constraint #4) X, Y ≥ 0 (non-negativity constraints)(a) Which of the constraints is redundant? Constraint #______.Justify by drawing a graph similar to Figure 7.14 on p.263.(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints).Constraint #1: _______________________________________________________________Constraint #2: _______________________________________________________________Constraint #3: _______________________________________________________________Constraint #4: ______________________________________________________________Consider the following LP problem with two constraints: 18X + 8Y >= 144and 9X + 4Y= 36. The objective function is Min 14X + 30Y . What combination of X and Y will yield the optimum solution for this problem? a. infeasible problem b. unbounded problem c. 0 , 9 d. 4 , 0 e. 2 , 4.54. Consider the following linear programming problem: Maximize Z=$15x + $5y, subject to (1) 2x + y ≤ 10 and (2) 4x + 3y ≤ 24 and (3) x, y ≥ 0. Will the optimal solution change if the objective function becomes Maximize Z=$15x + $20y (constraints remain the same)? Select one: a. Can't determine given the information. b. Yes, it will change. c. No, it remains the same.
- A Linear programming problem has the following three constraints: 30X + 14Y <= 420; 18X + 8Y= 144; and 19X - Y <= 67 . The objective function is Min 22X + 20Y . What combination of X and Y will yield the optimum solution for this problem? a. 0 , 18 b. unbounded problem c. infeasible problem d. 8 , 0 e. 4 , 9Given the following 2 constraints, which solution is a feasible solution for a minimization problem? (1) 7 x1 + 3 x2 ≥ 21 (2) x1 + 3 x2 ≥ 6 Group of answer choices (x1, x2) = (2, 5) (x1, x2) = (1, 2) (x1, x2) = (0, 4) (x1, x2) = (0.5, 5)