Pls help me formulate a linear programming model for this problem. Pls state the
ID: 408470 • Letter: P
Question
Pls help me formulate a linear programming model for this problem. Pls state the following respectively:
1. Decision Variables
2. Objective function
3. Constraints
22. The maintenance division of Speedy Taxi Company needs the following quantities of automobile generators for the next three months Month Generator Requirement 100 150 200 It can purchase a new generator for P400 or have a used generator rebuilt by an outside firm for P250. In the latter case the outside firm picks up the used generators at the beginning of the month and returns the rebuilt generators at the beginning of the following month. The taxi company has 120 used generators in stock, but the used generators will not have any salvage value at the end of three months. If possible, the company wants to avoid storing any used generators. How can the taxi company minimize the total cost of meeting the generator requirements for the three-month period?Explanation / Answer
Decision variables: a,b,c,d,e,f. Where,
a, b : first month's new and used generator quantities respectively
c,d : second month's new and used generator quantities respectively
e,f : third month's new and used generator quantities respectively
Objective function : Minimize {400 (a+c+e) + 250 (b+d+f)}
Constarints:
a,b,c,d,e,f>=0
a+b=100
c+d=150
e+f=200
Since 120 used generators are in stock they need to be rebuilt and they can used after a month i.e. in 2nd month hence,
d<=120
similarly, the generators from the month 1, will be used in third month, hence,
f<=100