Use the Big-M method to find an initial basic feasible solution for the following LP: max z = 3xị + x2 X1 + x2 2 3 2x1 + x2 < 4 X1 + x2 = 3 X1, X2 2 0 s.t.
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please do not use an online solver, they confuse me more than anything.
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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.)If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
- Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 17x + 19y subject to 8x + 14y ≥ 21 11x + 6y ≥ 31 and x ≥ 0, y ≥ 0. What is the optimal value of x and y? What is the minimum value of the objective function? Please show me step by step how to do this by hand, not through excel.Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = 13x + 3y subject to 12x + 14y ≤ 21 15x + 20y ≤ 37 and x ≥ 0, y ≥ 0. What is the optimal value of x?Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 11x + 5y + 10z subject to 8x + 12y + 19z ≥ 68 13x + 16y + 5z ≥ 136 and x ≥ 0, y ≥ 0, z ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the optimal value of z? What is the minimum value of the objective function?
- Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Maximize C = 14x + 13y + 5z subject to 9x + 11y + 18z ≤ 61 14x + 15y + 12z ≤ 122 and x ≥ 0, y ≥ 0, z ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the optimal value of z? What is the maximum value of the objective function?Find the indicated maximum or minimum value of the objective function in the linear programming problem. Minimize g = 10x + 6y subject to the following. x + 2y ≥ 10 2x + y ≥ 11 x + y ≥ 9 x ≥ 0, y ≥ 0Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 8x + 8y subject to 7x + 9y ≥ 16 10x + 10y ≥ 22 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the minimum value of the objective function?
- Use the graphical method to solve the following problem: max Z = 2x1 + x2 subject to: 3x1 + x2 ≤ 44 2x1 + 5x2 ≥ 60 x1 + x2 ≤ 18 x2 ≤ 10 x1, x2 ≥ 0Find the optimal solution for the following problem. Maximize C = 4x + 12y subject to 3x + 5y ≤ 12 6x + 2y ≤ 10 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? (Round your answer to 3 decimal places.) What is the maximum value of the objective function? (Round your answer to 3 decimal places.)Solve the following LP by using Excel. State the Optimal Solution and the Objective Function Value. Maximize profit = 910X + 1000Y Subject to: 18X + 20Y ≤ 1,200 360X + 400Y ≤ 30,000 X, Y ≥ 0