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- Two law students, John and Marsha, are planning an all-nighter to prepare for theirlaw boards the following day. Between them they have one set of materials in thefollowing five subjects: contracts, torts, civil law, corporate law, and patents.Based on their previous experience, they estimate that they will need the following amount of time (in hours) with each set of materials:Contracts Torts Civil Corporate PatentsJohn 1.2 2.2 0.7 0.5 1.5Marsha 1.8 0.8 3.1 1.1 2.3They agree that Marsha will get the opportunity to see each set of notes beforeJohn. Assume that they start their studying at 8:00 P.M. Determine the exact timesthat each will begin and end studying each subject in order to minimize the totaltime required for both to complete studying all five subjectsFour jobs are to be assigned to employees. There are 5 available employees. Durations for each job/employee combination are given in the following table. Build an assignment model to minimize the total time. What is the minimum optimal time? Employees Jobs 1 2 3 4 5 A 15 20 18 28 16 B 16 25 14 18 20 C 25 30 27 32 17 D 32 25 20 26 20May I have the linear programming graph (or model) or plot with the given following information? 3 variables and 8 contraints Objective - Zmax = 1.85R+2.1D+2.15H Constraints: 0.15R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.15H ≤ 7500 0.25R + 0.2D + 0.15H ≤ 7500 0.10R + 0.2D + 0.25H ≤ 6000 0.25R + 0.2D + 0.20H ≤ 7500 R ≥ 10000 D ≥ 3000 H ≥ 5000
- Exercise 4 a) Write the objective function of this LP.b) Write the constraint of the basic element Y.c) Write the constraint that expresses"the factional contributions from each mine must add up to 1."d) What is the optimal fraction of a ton to be chosen from mine 4?e) To make the optimal fraction of a ton to be chosen from mine 4 non-zero, how should the cost per ton of ore from mine 4 change?f) If the minimum requirement amounts of basic element X increases to 7 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?g) If the minimum requirement amount of basic element Z decreases to 25 tons, how much does the cost of a feasible blend (i.e., the value of the objective function) become?Consider the following linear program. Max 1A + 2B s.t 1A≤ 4 1B≤ 3 2A + 2B = 10 A, B ≥ 0 (a) Show the feasible region. (b) What are the extreme points of the feasible region? (b) What are the extreme points of the feasible region? smaller x-value (A, B) = (______) larger x-value (A,B)= (_____) (c) Find the optimal solution using the graphical procedure. (A, B) = (______)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 = 5
- Find the optimal solution to this linear programming problem. Min 5X + 6Y s.t. 3X + Y ≥ 15 X + 2Y ≥ 13 3X + 2Y ≥ 31 X, Y ≥ 0ou are given a linear programming problem. Maximize P = 3x + 3y subject to 5x + 3y ≤ 30 Resource 1 2x + 3y ≤ 21 Resource 2 x ≤ 4 Resource 3 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1.Task 4In this task, you are asked to formulate the linear programming problem below andthen solve it.A carpenter produces Tables (T) and Chairs (C).Each Table unit requires 6kg of wood and 1kg of plastic.Each Chair unit requires 4kg of wood and 4kg of plastic.The carpenter has only 100kg of wood and only 50kg of plastic in stock.On each sale, the carpenter makes a profit of £15 per Table unit sold and a profit of£30 per Chair unit sold.Required:Formulate the Linear Programming problem above by defining the variables,stating the object function and the constraints.You are required to produce the graph for all inequalities (copy image to Word)Find the quantity to make of Tables and Chairs to maximise profit.
- Consider a small Oil production firm with 5 competing oil production projects, A - E. The table below shows the estimated long-term profit (Net Present Value) for each project as well as the amount of investment capital required to start the project. You have been contacted to help select the best combination of projects to maximize the Net Present Value subject to the capital investment limit of $32 million. Production Project A B C D E Estimated Profit (millions) 25 20 19 28 21 Capital Required (millions) 11 8 14 19 13 Formulate a Binary Integer Programming (BIP) model on a spreadsheet. Solver the model using Solver.develope a space matrix for macdonalds. Below are the instructions. The steps required to develop a SPACE Matrix are as follows: 1. Select a set of variables to define financial position (FP), competitive position (CP), stability position (SP), and industry position (IP). 2. Assign a numerical value ranging from +1 (worst) to +7 (best) to each of the variables that make up the FP and IP dimensions. Assign a numerical value ranging from -1 (best) to -7 (worst) to each of the variables that make up the SP and CP dimensions. On the FP and CP axes, make comparison to competitors. On the IP and SP axes, make comparison to other industries. 3. Compute an average score for FP, CP, IP, and SP by summing the values given to the variables of each dimension and then by dividing by the number of variables included in the respective dimension. 4. Plot the average scores for FP, IP, SP, and CP on the appropriate axis in the SPACE Matrix. 5. Add the two scores on the x-axis and plot the resultant…Ali has chosen improvement of commercial systems and security threat as a researchsubject for his Informatics Ethics course. He develops an algorithm for the purpose ofimplementing his project in a practical process. He can find the security vulnerabilities of thecompanies network systems with this algorithm. He releases that he can reach the securityvulnerabilities of some companies with this algorithm and he adds these vulnerabilities to hisproject as a result of semester’s work. His professor decides that Ali has done a good project andgives him a very high project grade. When one of the companies that Ali has entered searches thesource of the attack, they find university laboratory as a source of this attack and informs theauthorities of his university. Looking at the scenario discuss the justifications may be given byprofessor, Ali and the company. Keeping in mind company’s opinion, should Ali be punished bythe University? What will be the stance of the University?