B. A firm manufactures 2 product, A and B. Each product is processed by machines, M₁ andM2. Each unit of type A requires 1 hour of processing by M₁ and 2 hours in M and eachunit type of type B requires 3 hours on M₁ and 1 hour on M₂. The profit on product A isP20 per unit and on product B is P30 per unit. If M₁ is available for 200 hours each monthand M₂ for 300 hours, how many units of each type can be manufactured in one month inorder to maximize the profits?Requirement:1) Formulate the linear programming model2) Solve the linear programming using the graphical method

According to given information- Machine Product A (x) Product B (y) Time M1 1 3 200 M2 2 1…

Answered: B. A firm manufactures 2 product, A and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5. A manufacturing company makes two models A and B of a product. Each piece of Model A requires 12 labor hours for fabricating and 1 labor hour for finishing. Each piece of Model B requires 6 labor hours for fabricating and 3 labor hours for finishing. For fabricating and finishing, the maximum labor hours available are 150 and 60 respectively. The company makes a profit of $10000 on each piece of model A and $9000 on each piece of Model B. How many pieces of Model A and Model B should be manufactured per week to realize a maximum profit? What is the maximum profit per week?
WorldLight Company produces two lamp fixtures (products 1 and 2) that require metal parts and electrical components. Management wants to determine how many units of each product to manufacture to maximize profit. For each unit of product 1, 1 unit of metal parts and 2 units of electrical components are required. For each unit of product 2, 3 units of metal parts and 2 units of electrical components are required. The company has 200 units of metal parts and 300 units of electrical components. Each unit of product 1 yields a profit of $1 and each unit of product 2, up to 60 units, yields a profit of $2. Any excess of 60 units of product 2 does not yield a profit, so making more than that amount is out of consideration. a) Formulate a linear programming model. b) Use the graphical method to solve this model. What is the resulting total profit?
A company manufactures two products, A and B, on two machines, I and II. It has been determined that the company will realize a profit of $3/unit of Product A and a profit of $4/unit of Product B. To manufacture 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture 1 unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit? Product A units units Product B What is the largest profit the company can realize? $ Is there any time left unused on the machines? (If so, give the number of minutes remaining. If not, enter 0.) Machine I min Machine II min
A firm manufactures two types of shafts A and B. For any month it must produce 250 shafts A and 100 shafts B. The maximum total requirement of shafts A and B is 1,250 and minimum total requirement is 500. Both shafts are to be processed on machines M1 and M2. Total number of machines M1 and M2 available are 15 each. Processing times in hours for each shaft on machines M1 and M2 are as follows: A B M1 1.5 2 M2 1 1.5 Profit/unit (K) 400 600 If the firm has 25 working days a month, each of 8 hours, Formulate the linear programming model for the problem. Solve the problem by graphical method.
A company manufactures two products A and B, and each of these products must be processed on two different machines. Product A requires 1 minute of work time per unit on machine 1 and 4 minutes of work time on machine 2. Product B requires 3 minute of work time per unit on machine 1 and 2 minutes of work time on machine 2. Each day 100 minutes are available on machine 1 and 200 minutes are available on machine 2. The profit of each unit of product A is $50 and the profit of each unit of product B is $60. (Let x = number of units of product A and y = number of units of product B). 1. Identify the variables. 2. Set up the objective function. 3. Give the constraints in mathematical expression. 4. Graph the constraints and identify the solution. 5. How many units of each product should be produced daily in order to maximize the company's profit? 6. What is that maximum profit daily?
A company manufactures two products, A and 3, in 2 factories, I and II. It has been determined that the company will realize a profit of 75 dollars on each unit of product A and a profit of 70 dollars on each unit of product B. To manufacture a unit of product A requires 7 minutes in factory I and 8 minutes in factory II. To manufacture a unit of product B requires 9 minutes in factory I and 5 minutes in factory II. There are 675 minutes of machine time available in factory I and 560 minutes of machine time available in factory II per day. How many units of each product should be produced per day to maximize the company's profit? units per day of product A, and units per day of product B. The maximal achievable profit is dollars per day. Now assume that, due to changing market conditions, the company can now realize a profit of 116 dollars on each unit of product A, whereas the profit on product B remains the same as before. How many units of each product should now be produced per day…
The company wants to find its daily production program maximizing its daily sales. These are made up of sales from individual types of fumiture. The company will receive CZK 500 for each chair produced, CZK 1,500 for a dining table and CZK 3,000 for each bed. Daily furniture production is stored in a warehouse with a size of 220 m2 The chairs occupy 0.5 m2, dining tables 2 m2 and beds 4 m2. The production of one chair takes 1 hour of work, the production of a dining table takes 2 hours and the bed takes 5 hours to produce due to its complexity. In total, there is a working hours capacity corresponding to the number of employees Long-term contracts with customers require that at least 10 beds be made per day. How much of chairs, dinning tables and beds have to be optimally produced daily ?
A company manufactures two, A and B, on two machines, 1 and 2. It has been determined that the company will realize a profit of $3/unit on Product A and a profit of $4/unit on product B. To manufacture 1 unit of Product A requires 6 min on Machine 1 and 5 min on Machine 2. To manufacture 1 unit product of Product B requires 9 min on Machine 1 and 4 min on Machine 2. There are 5 hr of machine time available on Machine 1 and 3 hr of machine time available on Machine 2 in each work shift. How many units of each product should be produced in each shift to maximize the company's profit? What is the largest profit the company can realize? Is there any time left unused on machines?
Assume that the production of 1 unit of magnesium requires 0.8 units of magnesium and 0.2 units of aluminum, and that the production of 1 unit of aluminum requires 0.3 units of magnesium and 0.2 units of aluminum.
A company manufactures three types of leather belts, namely A B and C. The unit profits from these three varieties are 10, 5 and 7 respectivel Leather is sufficient for only S00 belts per day (all types together) Belt A requires thrice the time of belt B and belt C requires twice the time of B. If all the belts of type B are produced, a maximum of 1,000 belts per day can be produced. Belt A requires a fancy buckle and 150 such buckles per day are availlable. There are sufficient number of buckles for the other varieties. Determine using simplex method, how many belts of each type be produced to maximize the total profit.
A company produces 3 products. Each unit of product 1, 2, and 3 generate a profit of GH₵10, GH₵12, and GH₵12 respectively. Each product has to go through a manufacturing, assembly, and testing phase. The company’s resources are such that only 20 hours of manufacturing, 20 hours of assembly, and 20 hours of testing are available. Each unit of product 1 has to spend 1 hour in manufacturing, 2 hours in assembly, and 2 hours in testing. Each unit of product 2 has to spend 2 hours in manufacturing, 1 hour in assembly, and 2 hours in testing. Each unit of product 3 has to spend 2 hours in manufacturing, 2 hours in assembly, and 1 hour in testing. Company ABC wants to know how many units of each product it should produce, in order to maximize its profit.a) Formulate a linear programming model for this problem.
A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $1, and each Type B souvenir will result in a profit of $1.20. To manufacture a Type A souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 3 hours available on Machine I and 5 hours available on Machine II. (a) The optimal solution holds if the contribution to the profit of a Type B souvenir lies between $ 48 X and $ 96 X. (Enter your answers from smallest to largest.) (b) Find the contribution to the profit of a Type A souvenir (with the contribution to the profit of a Type B souvenir held at $1.20), given that the optimal profit of the company will be $196.80. $2 (c) What will be the optimal profit of the company if the contribution to the profit of a Type B souvenir is $1.50 (with the contribution to the profit of a Type A souvenir held at $1.00)? $168

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