Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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The Touche Young accounting firm must complete three jobs during the next month. Job 1 will require 500 hours of work, job 2 will require 300 hours of work, and job 3 will require 100 hours of work. Currently, the firm consists of 5 partners, 5 senior employees, and 5 junior employees, each of whom can work up to 40 hours per month. The dollar amount (per hour) that the company can bill depends on the type of accountant who is assigned to each job, as shown in the table below. (The X indicates that a junior employee does not have enough experience to work on job 1.) All jobs must be completed. Touche Young has also set the following goals, listed in order of priority:
Goal 1: Monthly billings should exceed $68,000.
Goal 2: At most, 1 partner should be hired.
Goal 3: At most, 3 senior employees should be hired.
Goal 4: At most, 5 junior employees should be hired.
Formulate a preemptive goal programming model for thissituation
IKEO is a furniture manufacturer which produces two sizes of wood blocks (type A and B) thatare used to make either a table or a chair. A table is made of a type A and a type B wood blocks,while a chair is made of a type A and two type B wood blocks (See Figure 1)
A table makes RM 3 profit, and a chair makes RM 5 profit. If M number of type A and Nnumber of type B wood blocks are produced, how many tables and chairs should themanufacturer make to obtain the greatest profit?For example, let M = 12 and N = 12.By making 4 tables (4 type A and 4 type B) and 4 chairs (4 type A and 8 type B), themanufacturer gain profit as follows,Profit = (RM 3) × 4 + (RM 5) × 4 = RM 32.If the manufacturer makes 2 more tables and 1 less chair, the profit will be increased as follows,Profit = (RM 3) × 6 + (RM 5) × 3 = RM 33.Is this the greatest profit?
Write a complete C++ program to help the manufacturer determine the greatest profit obtainfrom making tables and chairs with a given number of M type A and N…
A firm is considering projects A, B, . . . , H. Using binary variables x_a, ..., x_h and linear constraints, model the following conditions on the projects to be undertaken.
At most one of A,B,...,H.
Exactly two of A,B,...,H.
If A then B.
If A then not B.
If not A then B.
If A then B and C.
If A then B, and if B then A.
If A then B or C.
If B or C then A.
If B and C then A.
If two or more of B,C,D,E then A.
If m or more than n projects B,...,H then A.
Chapter 9 Solutions
Introduction to mathematical programming
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- HOMEPRO is a furniture manufacturer which produces two sizes of wood blocks (type A and B) thatare used to make either a table or a chair. A table is made of a type A and a type B wood blocks,while a chair is made of a type A and two type B wood blocks (See Figure 1) A table makes RM 3 profit, and a chair makes RM 5 profit. If M number of type A and Nnumber of type B wood blocks are produced, how many tables and chairs should themanufacturer make to obtain the greatest profit?For example, let M = 12 and N = 12.By making 4 tables (4 type A and 4 type B) and 4 chairs (4 type A and 8 type B), themanufacturer gain profit as follows,Profit = (RM 3) × 4 + (RM 5) × 4 = RM 32.If the manufacturer makes 2 more tables and 1 less chair, the profit will be increased as follows,Profit = (RM 3) × 6 + (RM 5) × 3 = RM 33.Is this the greatest profit? Write a complete C++ program to help the manufacturer determine the greatest profit obtainfrom making tables and chairs with a given number of M type A and…arrow_forwardABC Company produces three electrical products—blenders, choppers, and toasters. The manufacturer has a maximum daily production budget of RM2000 and a maximum of 660 hours of labor. Maximum daily customer demand is for 200 blenders, 300 choppers, and 150 toasters. The unit profit for blender is RM8, choppers, RM10, and toaster, RM7. The company desires to know the optimal product mix that will maximize profit. These products have the following resource requirements as shown in Table 1. Based on the report, answer the following questions and justify all your answers. Formulate the LP model for the above case study. Optimize the Company ABC production using linear programming simplex method. Suppose that the company would like to increase the profit of the toasters to RM9 per unit without affecting the optimum number of products to be produced based on earlier conditions. Based on the Sensitivity Report, advise the company if this can be accomplished and justify your answer. If this…arrow_forwardABC Company produces three electrical products—blenders, choppers, and toasters. The manufacturer has a maximum daily production budget of RM2000 and a maximum of 660 hours of labor. Maximum daily customer demand is for 200 blenders, 300 choppers, and 150 toasters. The unit profit for blender is RM8, choppers, RM10, and toaster, RM7. The company desires to know the optimal product mix that will maximize profit. These products have the following resource requirements as shown in Table 1. Based on the report, answer the following questions and justify all your answers. Formulate the LP model for the above case study. Suppose that the company would like to increase the profit of the toasters to RM9 per unit without affecting the optimum number of products to be produced based on earlier conditions. Based on the Sensitivity Report, advise the company if this can be accomplished and justify your answer. If this can be done, what would be the company’s profit based on new pricing. The…arrow_forward
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