Concept explainers
To solve: The following linear programming problem graphically.
Introduction:
Linear programming:
It is a linear optimization technique followed to develop the best outcome for the linear programming problem. The outcome might be to maximize profit, minimize cost, or to determine the optimal product mix. The outcome will take the constraints present in achieving the solution into consideration.
Iso-cost line method:
The iso-cost line method is a technique used to find the optimal solution of a linear programming problem. A parallel line is drawn and moved downward, towards the axis, until it touches the last corner point in the feasible region which has the lowest cost.
Want to see the full answer?
Check out a sample textbook solutionChapter B Solutions
Operations Management: Sustainability and Supply Chain Management (12th Edition)
- Solve the problemarrow_forwardA recruiter for a job placement agency is considering whether to pay $50,000 per year to lease a new recruiting facility in a prime location in Washington D. C. He estimates it will cost $50 per recruit to process the paperwork at this new location. He receives a $75 commission for each new recruit he processes. Part A - If the office space at this new location has design and effective capacities of 10,000 and 8,000 recruits processed annually, respectively, and 6,000 recruits will be processed per year, what will be the utilization of the office space?Part B - If his office space at this new location has design and effective capacities of 10,000 and 8,000 recruits processed annually, respectively, and he plans to be 90% efficient in his use of this space, how many recruits does he plan to process per year?arrow_forwardSensitivity analysis: what are the benefits of this application as it relates to linear programming?arrow_forward
- Can I have more details on where does numbers in a) come from: 0.30 × $1.75 - 0.70×$0.5arrow_forwardA department is preparing a trip for 80 volunteers to an area affected by the typhoon. The transportation company to transit the volunteers has 8 vans of 15 seats each and 5 vans of 10 seats, but only has 15 drivers available. The rental cost for a large van is $150 and $100 for a small van. Calculate how many vans of each type should be used for the trip for the least possible cost. Question 1: What objective function will be used to evaluate the minimum cost? Question 2: Given the feasible region, how many corner points does the LP model generate? Question 3: Given the graph of the LP model, which of the following is not a corner point? (0,0), (0,8), (0,15) (15,0) Question 4: How many constraints, excluding the non-negative constraints, will be considered for the determination of the optimal solution? Question 5: What is the minimum cost referred to in the problem?arrow_forwardBenny is the manager of an office-support business that supplies copying, binding, and other services for local companies. He must replace a worn-out copy machine that is used for black- and-white copying. He is considering two machines, and each of these has a monthly lease cost plus a cost for each page that is copied. Machine 1 has a monthly lease cost of $639, and there is a cost of $0.030 per page copied. Machine 2 has a monthly lease cost of $747, and there is a cost of $0.045 per page copied. Customers are charged $.08 per page copied. a. What is the break-even point for each machine? b. If Benny expects to make 75,000 copies per month, what would be the monthly cost for each machine? (round your answers to the highest whole number)arrow_forward
- A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: Customer (requirement) Factory (capacity) Customer 1 (25) Customer 2 (50) Customer 3 (125) Customer 4 (75) A (100) $ 15 $ 10 $ 20 $ 17 B (75) $ 20 $ 12 $ 19 $ 20 C (100) $ 22 $ 20 $ 25 $ 14 Note: This question requires Solver.Formulate the problem in Solver and find the optimal solution. What is the minimum total cost to meet all customer requirements?arrow_forwardBenny is the manager of an office-support business that supplies copying, binding, and other services for local companies. He must replace a worn-out copy machine that is used for black-and-white copying. He is considering two machines, and each of these has a monthly lease cost plus a cost for each page that is copied. Machine 1 has a monthly lease cost of $619, and there is a cost of $0.040 per page copied. Machine 2 has a monthly lease cost of $685, and there is a cost of $0.025 per page copied. Customers are charged $.12 per page copied. If Benny expects to make 75,000 copies per month, what would be the monthly cost for each machine?arrow_forwardThe Ace Manufacturing Company has orders for three similar products. Product Min A s.t. B C 1 2 Machine 3 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A A LB B Ic C Product 4 2 3 Orders (units) Machine 1 Capacity Product A Orders Machine 2 Capacity Product B Orders Machine 3 Capacity Product C Orders 1,800 X20 for all i, j. 700 1,100 Capacity (units) 1,400 (a) Develop the linear programming formulation of this problem. (Let x₁ be the number of units of product A produced by XA1 machine 1, x,, be the number of units of product i produced by machine j, etc.) 1,500 1,000 1 Machine $1.00 $1.30 $1.10 2 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 3 (b) Solve the transportation model for the…arrow_forward
- 1. UST 40,000 (Commerce 5,000; Medicine 15%; AB 20%; Law 5% and others) Average price per computer device Php25,000 Average price per Apple device Php30,000 In UST, students from Commerce, Law, and AB purchased at least one (1) computer device in December 2020. Given that students replace their computer devices once every 2 years on average, what is the projected market size (units/revenues) for computer devices for these colleges until the end of 2025? What is the concentration of sales/revenue of computer devices among the colleges (CDI)? Please include explanations and formulas. Thank youarrow_forwardThe Seaside Hotel is a three-star hotel in Newquay, Cornwall. It contains 108 rooms and employs 30 fulltime and 40 parttime personnel. Between May and August, the hotel's workforce is nearly doubled by casual and temporary workers. Cornwall is a difficult place to do business, especially in the tourism industry. Business is highly seasonal with hotels experiencing very low occupancy during the offseason and many hotels choose not to operate during this time. The Seaside Hotel operates all year round by supplementing its tourism trade during the off-season by offering discounted conferencing facilities for local businesses and as a cheap base for corporate events and activities, such as team building weekends. Tourism is, however, vitally important for the region and its businesses and provides a significant proportion of all jobs in the South West. Cornwall can, however, be a difficult place in which to work. For instance, Newquay – Cornwall’s most popular holiday destination – is one…arrow_forwardA company has fixed costs of $300,000 and produces one product with a selling price of $72.00and a variable cost of $42.00 per unit. The maximum factory capacity is 20,000 units and itanticipates selling 15,000 units. Determine the break-even point of operation.arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,