
Setting up equations
The production manager of a company needs to determine next month’s production plan for the company’s
ten products. The products use six resources: assembly line 1; assembly line 2; painting;
dryers; packaging; and storage. Storage is measured in m3, and the others are in hours. The requirements
for each product are:
Product Resource
1 2 3 4 5 6 7 8 9 10 Available
Assembly 1 2 1 0.5 0.75 1.5 0.25 0 0 0 0 2100
Assembly 2 0 0 0.3 0.45 0.5 0.65 1 0.8 2 3 1500
Painting 0 0.2 0 0.4 0.5 0.65 1.5 0.1 0.15 2 1000
Dryers 0 0.3 0 0.8 0.2 0 1 0.3 0.2 1 1000
Packaging 0.5 0.1 1 0.2 0.1 0.65 0.1 0.2 1 0.5 1600
Storage 0.25 0.1 0.5 0.45 0.4 0.25 0.1 0.1 2 0.3 1300
In addition, there are some company constraints which must be satisfied.
(i) There should be at most 4,500 units produced.
(ii) There should be at least two units of product 3 for every unit of the combined production of products 6 and 8 produced.
(iii) The total production of product 4 should be no more than the combined production of products
2 and 7.
(iv) The combined production of products 1 and 5 must be at most twice the production of product 9.
The profit contribution in dollars per unit for each of the ten products is 2.1, 3.2, 1.6, 4.8, 1.2, 4.3,
3.5, 1.8, 5.5, 3.9 respectively.
I just need to setup the equations and I am good. Here's what I have so far:
x1+x2+x3+x4+x5+x6+x7+x8+x9+x10 <= 4500 units
x4<+x2+x7
2 (x1 + x5) <= x9
2x3 = x6x8
Is that right? What about the other six equations? Also:
"Now suppose that the cost of storage ($2.50 per m3) has not been taken into account in the profits, given for each product, but we now wish to include it. Modify the models from (a) (just
show what’s different compared with (a)), with the amount of storage used becoming the eleventh variable, and solve the modified model using a spreadsheet."
Thanks
Ibrox