In Exercises 9-20, use the simplex method to solve the given linear programming problem. (In each case the objective function is to be maximized.) 11. Objective function: z = 5x₁ + 2x₂ + 8x3 Constraints: 2x₁4x₂ + x3 = 42 - 2x₁ + 3x₂x3 = 42 6x₁x₂ + 3x₂ = 42 X₁ X₂ X30
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- 4 For each of the following, determine the direction in which the objective function increases: a z = 4x, - x2 b z = -x, + 2x2 C z = -x - 3x2For the products A, B, C, and D, which of the following could be a linear programming objective function? Select one: a. Z = 1A + 2BC + 3D b. Z = 1A + 2AB + 3ABC + 4ABCD c. Z = 1A + 2B + 3C + 4D d. Z = 1A + 2B/C + 3DInnis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis' risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3. The higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specified that at least $300,000 be invested in the money market fund. Refer to the computer solution shown below. Optimal…
- minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2Use the simplex method to find the optimal solution. Assume all variables are nonnegative. Minimize f = 7x + 9y subject to the following constraints. x2 5 y ≤ 19 -x + y 2 2 X = y = f= Need Help? Submit Answer xxx Read ItCan the function f (x) = - x2 + 3x +2 be maximized?
- Simplex Method Write in normal form and solve by the simplex method, assuming x, to be nonnegative. 1. The owner of a shop producing automobile trailers wishes to determine the best mix for his three products: flat-bed trailers, economy trailers, and luxury trailers. His shop is limited to working 24 days/month on metal- working and 60 days/month on woodworking for these products. The following table indicates production data for the trailers. Usage per unit of trailer Flat-bed Economy Luxury Available resources 1 2 1 24 Metal work days Wood work days Contribution (Rx100) 60 4 6 2 14 132(a) The tableau is not optimal for either maximization or a minimization problem. Thus, when a non-basic variable enters the solution it can either increase or decrease Z or leave it unchanged, depending on the parameters of the entering non basic variable. Basic x1 X2 X3 X4 X5 X6 X7 X8 solution -5 4 -1 -10 620 X8 3 -2 -3 -1 1 12 X3 1 1 3 1 3 X1 1 -1 -4 (i)Categorize the variables as basic and non-basic and provide the current values of all the variables. (ii)Assuming that the problem is of the maximization type, identify the non- basic variables that have the potential to improve the value of Z. If each such 3 variable enters the basic solution, determine the associated leaving variable, if any, and the associated change in Z. (iii)Repeat part (b) assuming that the problem is of the minimization type. (iv)Which non basic variable(s) will not cause a change in the value of Z when selected to enter the solution? (b) Let xij be the amount shipped from source i to destination j in a 5X5…Use simplex method for linear programming. Show solution for each iteration table. Problem: A small firm that assembles computers is about to start production of two new types of personal computers. Each type will require assembly time, inspection time, and storage space. The amount of each of these resources that can be devoted to the production of the computers is limited. The manager of the firm would like to determine the quantity of each computer to produce in order to maximize the profit generated by sales of these computers. In order to develop a suitable model of the problem, the manager has met with design and manufacturing personnel. As a result of those meetings, the manager has obtained the following information: Type 1 Type 2 Profit per unit $60 $50 Assembly time per unit 4 hours 10 hours Inspection time per…
- For minimization linear programming problem, the simplex method is terminated when all values of: a. Z (NB) s0 Ob. None of them Z (NB) = 0 Z (NB) 2 0a. Which of the following best describes the meaning of the equation P(25) = 200? 1. When 200 calculators are sold, the profit is $25. II. When 200 calculators are sold, the profit is increasing at a rate of $25 per additional calculator III. When 25 calculators are sold, the profit is $200. IV. When 25 calculators are sold, the profit is increasing at a rate of $200 per additional calculatoWhich one of the following would be a valid objective function for linear programming? O A. Min7XY B. Min 4X+3Y+(2/3)z C. Max5X^2+6Y^2 D. All of the above are linear objective functions