Case 3.2 Sonoma Essay

1830 Words Feb 21st, 2013 8 Pages
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
cost |Total cost |Selling Price |Profit |
|Brand I |\$0.75 |\$0.167 |\$0.917 |\$8.25 |\$7.333 |
|Brand II |\$0.85 |\$0.100 |\$0.950 |\$7.00 |\$6.050 |

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 second 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 |
| |62440.00 |26760.00 | | |
|Objective fn |7.333 |6.050 |619770.520 | |
|Constraint1 |0.917 |0.950 |82679.480 |82681.000 |