Case 3.2 Sonoma
Answer
The problem is to be formulated as two integer programming problems, one for the first year and the other for the second year.
I Year Problem
Total fund available = $10,000
For convenience rename the brand Petite Sirah as Brand I and brand Sauvignon Blanc as Brand II
For Brand I the cost for grape is $0.80 per bottle and for Brand II the cost for grape is $0.70 per bottle.
It is given that one dollar spent for promoting Brand I produce a demand for 5 bottles and one dollar spent for promoting Brand II produce a demand for 8 bottles . This means the advertisement cost per bottle for Brand I is $0.20 and the advertisement cost per bottle for Brand II is $0.125.
The cost-profit structure of the two brands during the first year is as follows.
|Brand |Grape cost |Advt. cost |Total cost |Selling Price |Profit |
|Brand I |$0.80 |$0.20 |$1.00 |$8.00 |$7.00 |
|Brand II |$0.70 |$0.125 |$0.825 |$7.00 |$6.175 |
Suppose George decide to produce X bottles of Brand I and Y bottles of Brand II
Then the total profit function to be maximised is [pic]
Total amount required is [pic].
Hence the constraint on the funds becomes C1: [pic]
Further, it is given that the proportion of Brand I should be between 40% and 60%. The corresponding constraint becomes [pic] This can be expressed as two constraints as follows
C2: [pic]
C3: [pic]
Thus the first year problem can be expressed as the following integer programming problem.
Maximize [pic]
Subject to [pic] [pic] [pic] X and Y non-negative integers
Solution of the problem using Solver of MS Excel is as follows
| |X |Y |Function |limits
The problem is to be formulated as two integer programming problems, one for the first year and the other for the second year.
I Year Problem
Total fund available = $10,000
For convenience rename the brand Petite Sirah as Brand I and brand Sauvignon Blanc as Brand II
For Brand I the cost for grape is $0.80 per bottle and for Brand II the cost for grape is $0.70 per bottle.
It is given that one dollar spent for promoting Brand I produce a demand for 5 bottles and one dollar spent for promoting Brand II produce a demand for 8 bottles . This means the advertisement cost per bottle for Brand I is $0.20 and the advertisement cost per bottle for Brand II is $0.125.
The cost-profit structure of the two brands during the first year is as follows.
|Brand |Grape cost |Advt. cost |Total cost |Selling Price |Profit |
|Brand I |$0.80 |$0.20 |$1.00 |$8.00 |$7.00 |
|Brand II |$0.70 |$0.125 |$0.825 |$7.00 |$6.175 |
Suppose George decide to produce X bottles of Brand I and Y bottles of Brand II
Then the total profit function to be maximised is [pic]
Total amount required is [pic].
Hence the constraint on the funds becomes C1: [pic]
Further, it is given that the proportion of Brand I should be between 40% and 60%. The corresponding constraint becomes [pic] This can be expressed as two constraints as follows
C2: [pic]
C3: [pic]
Thus the first year problem can be expressed as the following integer programming problem.
Maximize [pic]
Subject to [pic] [pic] [pic] X and Y non-negative integers
Solution of the problem using Solver of MS Excel is as follows
| |X |Y |Function |limits