Premium Essay

Sonoma Wine

In: Business and Management

Submitted By ohhxsean
Words 869
Pages 4
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
Total amount required is .
Hence the constraint on the funds becomes C1:
Further, it is given that the proportion of Brand I should be between 40% and 60%. The corresponding constraint becomes This can be expressed as two constraints as follows
C2:

C3:

Thus the first year problem can be expressed as the following integer programming problem.
Maximize
Subject to

X and Y non-negative integers

Solution of the problem using Solver of MS Excel is as follows

X Y Function limits 4470.00 6703.00
Objective fn 7.000 6.175 72681.025
Constraint1 1.000 0.825 9999.975 10000.000
Constraint2 3.000 -7.000 -33511.000 0.000
Constraint3 6.000 -4.000 8.000 0.000

Analysis

Brand Qty to be produced Grape cost Advt. cost Total cost Revenue Profit
Brand I 4470.000 3576.000

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