a) Identify the basic variables. b) What is the value of x1? c) What is the value of x2? d) What is the value of x3? e) What is the value of P , the optimal solution?
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1Given the following transportation matrix where the numbers in the cells represent cost of transporting 1unit from a specific source to a specific destination, determine the initial solution using the 3 methods anddetermine the optimum solution by using the initial solution with the lowest value of Z.Use the pseudoinverse to find a least squares solution to Ax=b for the given matrix A and b.
- 5) If B arises from a matrix A by elementary row operations, what is the relationship between NS(A) and NS(B)?4- Which of the following is the basis of the Gaus-Jordan method used in the solution of linear equation systems? a)Conversion of coefficients matrix in the expanded matrix to cofactor matrix. B)Conversion of the coefficients matrix in the expanded matrix to the unit matrix. NS)Conversion of coefficients matrix in the expanded matrix to zero matrix. D)Conversion of the coefficients matrix in the expanded matrix to the additional matrix. TO)Conversion of coefficients matrix in the expanded matrix to lower or upper triangular matrix.An engineer is studying the mileage performance characteristics of 5 types of gasoline additives. In the road test he wishes to use cars as blocks; however, because of a time constraint, he must use an incomplete block design. He runs the balanced design with the five blocks that follow. Car Additive 1 2 3 4 5 1 NA 17 14 13 12 2 14 14 NA 13 10 3 12 NA 13 12 9 4 13 11 11 12 NA 5 11 12 10 NA 8 - Verify that this is a balanced incomplete block design - Obtain the estimates of the treatment means and the treatments effects
- 1) Tabulate the problem in a simplex matrix with the objective of minimizing crude prices. (P.S. Use letters’ w, x, y, z as your basic variables)A diabetic patient needs at least 40 units of Vit. A, at least 30 units of Vit. C, and atleast 30 units of Vit. E each day. Each brand X multivitamin capsule contains 4 units ofVit. A, 6 units of Vit. C, and 2 units of Vit. E; each brand Y capsule contains 5 units of Vit.A, 3 units of Vit.C, and 5 units of Vit. E. If each brand X capsule costs P6.00 and eachbrand Y capsule costs P9.00, how many capsules should the patient take each day tominimize the costs? Solve using graphical method. Show complete solution.Required:1. Formulate the following:a. Decision variablesb. Objective functionc. Constraints2. Graph3. Identify feasible region.4. Solve for the value of X and Y at each point.5. Decision.A company manufactures two products, A and B, and each of these products must be processed on two different machines. Product A requires 3 min of work time per unit on machine 1 and 2 min of work time per unit on machine 2. Product B requires 1 min of work time per unit on machine 1 and 5 min of work time per unit on machine 2. Each day 200 min are available on machine 1 and 300 min are available on machine2. To satisfy certain customers, the company must produce at least 20 units per day of product A and at least 10 units per day of product B. If the profit of each unit of product A is Php50 and the profit of each unit of product B is Php60, how many units of each product should be produced daily in order to maximize the company's profits?
- Determine the real number values of the constant a with which the matrix A= (14 a1) is positive definite. (numbers are supposed to be lined on top of each other and next to each other)MSA Computer Corporation manufactures two models of minicomputers, the Alpha 4 and the Beta 5. The firm employs five technicians, working 160 hours each per month, on its assembly line. Management insists that full employment (i.e., all 160 hours of time) be maintained for each worker during next month’s operations. It requires 20 labor hours to assemble each Alpha 4 computer and 25 labor hours to assemble each Beta 5 model. MSA wants to see at least 10 Alpha 4s and at least 15 Beta 5s produced during the production period. Alpha 4s generate $1,200 profit per unit, and Beta 5s yield $1,800 each. Determine the most profitable number of each model of minicomputer to produce during the coming month.Q1 2) In which of the four cases is the coefficient matrix A of the system non-singular? In which cases is it singular? (Look at the definition below the middle table at the bottom of the page (definition 3.11))