The Pet Food Company makes two products, Cat food and Dog Food This Company runs
ID: 669255 • Letter: T
Question
The Pet Food Company makes two products, Cat food and Dog Food
This Company runs two Production Units, Blending and Packing departments. The required time in each Production Unit per ton of each product is shown below:
Time for processing each Ton (hours)
Blending
Packaging
Cat Food
0.25
0.10
Dog Food
0.15
0.30
The Units are open for work for 8 hours per day.
The following ingredients are used to make Dog food: Meat, Fishmeal and Cereal. While the following are used to make Cat food: Cereal, ground stones and seeds.
The cost and composition of each of the ingredients is displayed below
Material Composition in Percent and Cost/ton
Trace
Minerals
Protein
Carbohydrates
Abrasives
Cost ($/ton)
Meat
12
10
1
0
600
Fishmeal
20
8
2
2
900
Cereal
3
30
0
0
200
Seeds
10
10
2
1
700
Stones
0
0
3
100
100
The minimum percentage composition requirements of the two products are shown in the following table:
Trace
Minerals
Protein
Carbohydrates
Abrasives
Seeds
Cat Food
5
18
1
2
10
Dog Food
11
15
1
0
0
Cat food sells for $750/ton and Dog food sells for $980 per ton. Assuming Pet Food Company can sell all that it makes,
Solve by Formulating LINDO script, constraints and variables.
(1) what should be the composition of Cat and Dog food and
(2) how many tons of each should be manufactured each day to maximize Pet Food’s daily profit?
Time for processing each Ton (hours)
Blending
Packaging
Cat Food
0.25
0.10
Dog Food
0.15
0.30
Explanation / Answer
Answer 1) The composition of Cat and Dog food is 88 and 56. i.e.; The composition is in the ratio of 11 : 7.
Answer 2) To maximize Pet food's daily profit of each day, the number of tons used for manufacturing is 500 tons.
i.e.; Number of tons manufacturing each day = Total cost / Total number of tons
= 2500 / 5 = 500 tons
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