Question

4. The Robinsons are planning a wedding and reception for their daughter, Rachel. Some of the most expensive items served at the reception and dinner are wine and beer. The Robinsons are planning on 400 guests at the reception, and they estimate that they need at least four servings (i.e., a glass of wine or bottle of beer) for each guest in order to be sure they won’t run out. A bottle of wine contains five glasses. They also estimate that more than 50% guests will prefer wine to beer. A bottle of wine costs $6, and a bottle of beer costs $1. The Robinsons have budgeted $1,500 for wine and beer. The caterer has advised them that typically 8% of the wine and 15% of the beer will be left over. Finally, the Robinsons want to minimize their waste (i.e., cost from unused wine and beer). How many bottles of wine and beer should the Robinsons order? (a) Formulate a linear programming model for this problem. (b) Graphically illustrate the feasible area and identify all the possible extreme points. (c) Solve the model – find the optimal solution points and the optimal objective function value

Answer 1

(a)

Let

W = No. of 'bottles' of wine
B = No. of 'bottles' of beer

Min Z = total loss = 0.08 W + 0.15 B

Subject to,

5W + B >= 400 or, 5W + B >= 400

(5W) >= 150%*(B) or, 5W - 1.5B >= 0

6W + 1B <= 1500

W, B >= 0

(b)

(c)

Extreme point	W	B	Z = 0.08W + 0.15B
A	160.714	535.714	93.21
B	250	0	20.00
C	80	0	6.40
D	48	160	27.84

The optimal solution is at W = 80 and B = 0

Max. Z = 6.40 bottles of loss.