A logistics specialist for Charm City Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:
Assembly Plant
1 2 3 Supply
__________________________________________________________________
A 6 10 14 200
Factory B 2 2 6 400
C 2 8 7 200
__________________________________________________________________
Demand 220 320 200
The specialist wants to distribute at least 100 cases of parts from factory B to assembly plant 2.
(a) Formulate a linear programming problem to minimize total cost for this transportation problem.
(b) Solve the linear programming formulation from part (a) by using either Excel or QM for Windows. Find and interpret the optimal solution and optimal value. Please also include the computer output with your submission.
The following questions are mathematical modeling questions. Please answer by defining decision variables, objective function, and all the constraints. Write all details of the formulation. Please do NOT solve the problems after formulating.
Project Votes/dollar
________________________
Parks 0.07
Education 0.08
Roads 0.09
Health Care 0.11
Family Welfare 0.08
In order to also satisfy some local influential citizens, he must meet the following guidelines.
None of the projects can receive more than 30% of the total allocation.
The amount allocated to education cannot exceed the amount allocated to health care.
The amount allocated to roads must be equal to or more than the amount spent on parks.
All of the money must be allocated.
Formulate a linear programming model for the above situation by determining
(a) The decision variables
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.
Note: Do NOT solve the problem after formulating.
Medium | Cost Per Ad | Number Reached |
TV | 8500 | 12000 |
Radio | 1800 | 4000 |
Newspaper | 2400 | 5500 |
Magazine | 2200 | 4500 |
The number of TV ads cannot be more than 4. Each of the media must have at least two ads. The total number of Magazine ads and Newspaper ads must be more than the total number of Radio ads and TV ads. There must be at least a total of 12 ads. The advertising budget is $50,000. The objective is to maximize the total number reached.
Formulate a linear programming model for the above situation by determining
(a) The decision variables
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.
Note: Do NOT solve the problem after formulating.
Region (days)
Salesperson I II III
________________________________________
A 11 18 12
B 11 15 14
C 10 14 16
However, because of his health reason, salesperson C does not want to be assigned to region II.
The Company wants to assign either salesperson A or salesperson C to region I. The objective is to minimize total time of covering the three sales regions.
(a) The decision variables
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.
Note: Do NOT solve the problem after formulating.
Net Present Capital Requirements ($)
Alternative Value ($) Year 1 Year 2 Year 3
_____________________________________________________________
Warehouse expansion 30,850 32,000 12,000 38,000
Test market new product 92,300 58,000 41,000 45,000
Advertising campaign 40,000 25,000 12,500 11,800
Research & Development 82,000 53,000 13,000 44,000
Purchase new equipment 33,000 12,500 4,500 8,900
_____________________________________________________________
Capital funds available 110,500 65,000 88,750
The company wants to select at least 3 alternatives. In aIDition, the company also wants to select at least two alternatives from the warehouse expansion, research & development and purchase new equipment alternatives.
Develop a capital budgeting problem to maximize the total net present value in this situation.
Please answer by defining decision variables, objective function, and all the constraints. Write all details of the formulation. Please do NOT solve the problem after formulating.
Jodi is not sure how many miles she will drive over the next three years for this business but she believes it is reasonable to assume that she will drive 10,000 miles per year, 14,000 miles per year, or 18,000 miles per year. With this assumption, Jodi estimated her total profit for the three lease options. The three lease options and the associated profits for each are given below:
Dealer 10000 Miles 14000 Miles 18000 Miles
A $ 7000 $10500 $13500
B $ 8500 $11500 $11000
C $10000 $ 9500 $ 9800
Determine the optimal decision to lease the car from a dealer and the profit associated with it by using the following decision criteria.
a.Maximax
b.Maximin
c.Equal likelihood
a.Compute the expected value for each decision and select the best one.
b.Compute the expected regret value for each decision and select the best one.
? = 12.1 customers per hour
µ = 14.5 customers per hour
Determine P0, P1, P4, L, Lq, W, Wq, and U.
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