A person wants to decide the constituents of a diet which will fulfil his dai y requirements of proteins, fats and carbohydrates at the minimum cost. The choice is to be made from four different types of foods. The yields per unit of these foods are given in the following Table.
|
Food type
|
Yield per unit
|
Cost/unit
($)
|
|
Proteins
|
Fats
|
Carbohydrates
|
|
I
|
30
|
20
|
60
|
2
|
|
2
|
40
|
50
|
40
|
2
|
|
3
|
40
|
40
|
50
|
2
|
|
4
|
60
|
50
|
40
|
3
|
|
Min
requirements
|
800
|
500
|
700
|
|
The objective is to find the mixture of food types that will minimize the total cost while meeting the minimum requirements.
The LP model is shown below:
Min 2 xl +2 x2 +2 x3 +3 x4
ST
30 xl + 40 x2 + 40 x3 + 60 x4 >= 800 Proteins
20 xl + 50 x2 + 40 x3 + 50 x4 >.= 500 Fat
60 xl + 40 x2 + 50 x3 + 40 x4 >s, 700 xl , x2 , x3 , x4 >= 0 and integer Carbohydrates
The excel model is available under the name Prob3_Ans in the exam folder on Blackboard.
Answer the following Questions:
I) What are the basic variables? Non-basic variables?
2) What are the binding constraints? Non-binding constraints?
3) How many units of proteins, fats and carbohydrates will be available during the plan?
4) Construct a one way solver table for the effect of the cost per unit for food type 1 on the units of food I and the total cost. Test the values from 0 to 5 with increments of 0.5. Comment on the findings.
5) Construct a two way solver table for the effect of the cost per units for food type 2 and the cost per unit of food 4 on the total cost Test the values from 0 to 5 with increments of 0.5. Comment on the findings.
6) Resolve the problem by deleting the integer constraint. What is the effect of removing this constraint on the decision variables and the total cost?