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a. Discuss two Real-world example of the Linear Programming problems below.
production planning
resource allocation
Linear programming is a mathematical method that optimizes resource allocation to achieve a specific goal, despite various constraints.Linear programming aids organizations in making data-driven decisions, enabling efficient resource allocation and achievement of their objectives.
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- 2. A company manufactures two products A and B. Each unit of A requires 4 labour hours of processing and each unit of B requires 2 labour hours of processing. Demand for these two products per month is 7 and 10 units respectively Profit Per unit is Rs. 400 and Rs. 200 respectively. Determine the best combination of A and B to be produced. Total labour hours available per month is 32. There is additional cost of Rs. 200 per overtime labour hours and Rs. 175 cost of underutilised labour hours. A cost of Rs. 250 is assessed for any shortfall in meeting demand. The company has established the following goals and has assigned three priorities P1, P2, P3, P4 and P5, where P1 is of highest priority. P1: Maximise Total profit P2: Avoid underutilisation of labour P3: Meet Demand for Product A P4: Meet Demand for Product B P5: Do not use any overtimeNorthwest Pipe (NP) makes water pipe. NP is planningproduction for the next seven months, March through September.Th e forecast demands (in thousands of feet) are, respectively, 40,60, 70, 80, 90, 100, and 80. NP can make 75,000 feet of pipe permonth using regular-time production, at a cost of $1.25 per foot.Th ey can make up to an additional 15,000 feet using overtimeproduction at a cost of $1.50 per foot. Any pipe made in onemonth and sold in a later month incurs an inventory holding costof $0.15 per foot, per month. NP expects to end February with5000 feet of pipe and would like to plan to end September with10,000 feet in inventory. NP would like to plan their productionschedule to minimize total cost during the next seven months. (a) Formulate an LP to minimize total costs.(b) Set up and solve the problem on a spreadsheet.(c) What is the optimal solution? Explain the rationale for thesolutionfind the a. decision variables b. objective function c. constraints
- A college provides free tutoring services for its students 7 days a week, and the daily requirements for tutors are: Day M T W Th F S Su Requirements 5 4 7 3 6 3 4 Find the minimum number of tutors required if each tutor works 4 days a week and has 3 consecutive days off. Give preference to Saturday and Sunday off in case of a tie. (Hint: Look for group of 3 days with the lowest requirements). Specify the work schedule for each tutor. How much slack does your schedule generate for each day?Amy plans to start at least two different business activities after she graduates from college: − One business involves using various forms of social media to promote her skills and experience as a volleyball player to help younger players develop their skills She plans to generate income from advertising on her social media sites − She will also use her artistic and marketing talents to find work using several web platforms, like Upwork and Freelancer Although still in college, she has signed a “name, image, and likeness (N I L)” contract with several volleyball-related businesses. Amy also plays for U.S.A. Volleyball and was a member of the 2021 U.S.A. Olympic team Based on what she has read on websites and heard from friends, Amy is wondering if she should form a corporation or a limited liability company for these pursuits, or just be a sole proprietor. Also she is also curious whether, for tax and legal purposes, she has one business or two? Question: After reading this…NO. 5 Jenny Company produces two types of pants: long pants and short pants. The cost of making a pair of short pants and a pair of long pants are RM 75 and RM 95 respectively. In one week, the company must produce at least 150 pants of cach type. The minimum weekly production is 500 pants. The short pants is sold for RM 120 cach and the long pants for RM 150 cach. Using the graphical method, find: a) The number of short pants and long pants to be made in a week in order to minimize the total production cost. b) The profit made at the minimum weekly production cost.
- Sales & Operations Planning - LP A local firm manufactures children's toys. The projected demand over the next four months for one particular model of toy robot is given in the following table. Month Workdays Demand January 23 3800 February 16 7200 March 20 2800 April 22 4400 Assume that a normal day is eight hours. Hiring costs are $350 per worker and firing costs are $850 per worker. Holding costs are $4 per unit held per month. Additionally, assume that it requires an average of two hours for one worker to assemble one toy. Shortages are not permitted. It is given that the ending inventory for December was 900 of these toys and the manager wishes to have at least 800 units on hand at the end of April. Assume that the current workforce level is 35 workers. The firm wants to minimize its cost. Answer the following questions. 1. Formulate the problem as a linear program. For simplicity, use the number from the questions instead of introducing parameter notations. Clearly define your…2) Martha Manufacturing makes three products. Each product tequires manufacturing operations in three departments. A, B, and C. The labor-bour requirements, by department, are as follows: Department Product 1 Product 2 Product 3 A. 13 19 130 B 1.0 0.75 220 125 0.5 20 During the next production penod, the labor-houes available are 330 m department A. 350 in department B, and 200 in department C. The profit contributions per unat are S32 for productl. $28 for product 2, and $35 for product 3 a) Formulate a linear programming model for maxımızing total profit contrabution. b) Solve the linear program formulated in part (a) using excel How moch of each product should be produced, and what is the projected total profit contribution?How much influence can the employee requirements for one, two, or three days have on the weekly schedule in the employee scheduling example? Explore this in the following questions: a. Let Monday’s requirements change from 17 to 25 in increments of 1. UseSolverTable to see how the total number of employees changes.b. Suppose the Monday and Tuesday requirements can each, independently of one another, increase from 1 to 8 in increments of 1. Use a two-way SolverTable to see how the total number of -employees changes.c. Suppose the Monday, Tuesday, and Wednesday -requirements each increase by the same amount, where this increase can be from 1 to 8 in -increments of 1. Use a one-way SolverTable to -investigate how the total number of employees changes.
- Gerald Glynn manages the Michaels Distribution Center. After careful examination of his database information, he has determined the daily requirements for part-time loading dock personnel. The distribution center operates 7 days a week, and the daily part-time staffing requirements are Day M T W Th F S Su Requirements 7 3 5 5 6 2 2 Find the minimum number of workers Glynn must hire. Prepare a workforce schedule for these individuals so that each will have 2 consecutive days off per week and all staffing requirements will be satisfied. Give preference to the S-Su pair in case of a tie. (Note: If there is a tie that cannot be broken by following the preference to the S-Su pair, choose the pair closest to the beginning of the considered week.) Part 2 The minimum number of workers is _________workers. (Enter your response as a…I need help finding the answer for this problem3
