1.Production planning problem

A company manufactures four variants of the same product and in the final part of the manufacturing process there are assembly, polishing and packing operations. For each variant the time required for these operations is shown below (in minutes) as is the profit per unit sold.

Variant

Assembly

Polish

Pack

Profit in Rs.

1

2

3

2

1.50

2

4

2

3

2.50

3

3

3

2

3

4

7

4

5

4.50

  • Given the current state of the labour force the company estimate that, each year, they have 100000 minutes of assembly time, 50000 minutes of polishing time and 60000 minutes of packing time available. How many of each variant should the company make per year and what is the associated profit?
  • Suppose now that the company is free to decide how much time to devote to each of the three operations (assembly, polishing and packing) within the total allowable time of 210000 (= 100000 + 50000 + 60000) minutes. How many of each variant should the company make per year and what is the associated profit?


Reference:
http://people.brunel.ac.uk/~mastjjb/jeb/or/solvelp.html

2. Two Mines Company

The Two Mines Company own two different mines that produce an ore which, after being crushed, is graded into three classes: high, medium and low-grade. The company has contracted to provide a smelting plant with 12 tons of high-grade, 8 tons of medium-grade and 24 tons of low-grade ore per week. The two mines have different operating characteristics as detailed below.

Mine

Cost Per day (Rs.)

Production(tons/day)

High Low Medium
X
180
6 3 4
Y
160
1 1 6

How many days per week should each mine be operated to fulfill the smelting plant contract?

Construct a cost function, write down all the variables and constraints and solve it using Excel-solver. Make a readable excel sheet and upload it here.

Reference:
http://people.brunel.ac.uk/~mastjjb/jeb/or/basicor.html#twomines

Available from: Monday, 29 September 2008, 10:30 PM
Due date: Friday, 3 October 2008, 5:30 AM