min 8x1+6x2 subject to 4x1+2x2 ≥ 20 -6x1+4x2 ≤ 12 X1+X2 ≥ 6 X1, X2 20
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- Simplex problem Maximize: 10x1+6x2+3x3 S.t. X1+X2+2x3<=25 2x1+X2+4x3<=40 X1+2x2+3x3<=40 X1,X2,X3>=0Maximize: 500X1+300X2Subject to: 15X1+5X2≤30010X1+6x2≤240 8X1+12X2≤450 X1≥0,X2≥0Problem 3: Let L(x, y) be the statement “x loves y”, where the domain for both x and y consists of all people in the world. Use quantifiers to express each of the following statements.1. Everybody loves Jerry.2. Everybody loves somebody.3. There is somebody whom everybody loves.4. Nobody loves everybody.5. There is somebody whom Lydia does not love.6. There is somebody whom no one loves.7. There is exactly one person whom everybody loves.8. There are exactly two people whom Lynn loves.9. Everybody loves himself or herself.10. There is someone who loves no one besides himself or herself.
- A machine shop manufactures two types of bolts. The bolts require time on each of the three groups of machines, but the time required on each group differs, as shown in the table below. Type I Type IIMachine 1 0.2 min 0.2 minMachine 2 0.6 min 0.2 minMachine 3 0.04 min. 0.08 min Production schedules are made up one day at a time. In a day, 300, 720, and 100 minutes are available, respectively, on these machines. Type I bolts sell for 15¢ and type II bolts for 20¢. (a) How many of each type of bolt should be manufactured per day to maximize revenue?(b) What is the maximum revenue?(c) Suppose the selling price of type I bolts began to increase. Beyond what amount would this price have to increase before a different number of each type of bolts should be produced to maximize revenue?Given the following data on inputs and outputs at a work center, determine the cumulative deviation and the backlog for each time period. The beginning backlog is 7. (Negative amounts should be indicated by a minus sign.) Input Period 1 2 3 4 5 6 Planned 200 200 180 190 190 200 Actual 210 200 179 195 193 194 Output Period 1 2 3 4 5 6 Planned 200 200 180 190 190 200 Actual 205 194 177 195 193 200 1 2 3 4 5 6 Input Cumulative Deviation Output Cumulative Deviation Backlog 7Calculate the linear programming: Min. Z = 6X1+3X2 Constraints 2X1+4X2 ≥ 16 4X1+3X2 ≥ 24 X1,X2 ≥ 0
- 19. What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y, subject to (1) 2x + 3y ≤ 12 and (2) 5x + 2y ≤ 10 and (3) x, y ≥ 0. Part 2 A. x = 0, y = 3 B. x = 2, y = 0 C. x = 0, y = 0 D. x = 0, y = 4 E. x = 1, y = 51. Suppose you are going on a weekend trip to a city that is d miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you? 2. Suppose that a manager has a choice between the following two mathematical models of a given situation: (a)a relatively simple model that is a reasonable approximation of the real situation, and (b)a thorough and complex model that is the most accurate mathematical representation of the real situation possible. Why might the model described in part (a) be preferred by the manager?2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest. Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%. The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per P40,000 invested. The Diversified fund has a risk rating of 4 per P40,000 invested. For example, if P400,000 is invested in each of the two investment funds, Provident’s risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, Provident developed…
- Solve this using Simplex method Maximize: 4x1 + 2x2 + 5x3 S.t. x1 + 2x2 + x3 <=25 x1 + 4x2 + 2x3<=40 3x1 + 3x2 + x3 <= 30 x1, x2, x3>=02. A canning company produces two sizes of cans—regular and large. The cans are produced in 10,000-can lots. The cans are processed through a stamping operation and a coating operation. The company has 30 days available for both stamping and coating. A lot of regular-size cans require 2 days to stamp and 4 days to coat, whereas a lot of large cans requires 4 days to stamp and 2 days to coat. A lot of regular-size cans earn $800 profit, and a lot of large-size cans earn $900 profit. In order to fulfill its obligations under a shipping contract, the company must produce at least nine lots. The company wants to determine the number of lots to produce of each size can (and) in order to maximize profit. 8. In Problem 2, how much flour and sugar will be left unused if the optimal numbers of cakes and Danish are baked?Ping Sotto, an Overseas Filipino Worker, is planning to return to the Philippines. As an OFW for more than fifteen years and having established connections abroad, Ping Sotto is planning to establish his own recruitment and placement agency. If putting up his own recruitment and placement agency is not feasible, he is planning to apply for a job in a prestigious construction company in the country. Ping Sotto is planning to hire minimum wage employees for its newly formed recruitment and placement agency. What is a minimum wage?