Question

Formulate the following problem as an LP problem.

Glassco manufactures wine glasses, beer glasses, champagne glasses and whiskey glasses. Each type of glass uses time in the molding shop, time in the packaging shop and a certain amount of glass. The resources required to make one of each type of glass are given below.    At present, 600 minutes of molding time, 400 minutes of packaging time and 500 oz of glass are available per week. Glassco has a contract that must be met - to provide 20 beer glasses to a local bar.   Glassco wishes to maximize profit per week.

	Wine	Beer	Whiskey	Champagne
Molding time (min)	4	9	7	10
Packaging time (min)	1	1	3	40
Glass (oz)	3	4	2	2.5
Profit $	6	10	9	20

Answer 1

Since the only formulation is required, we need not solve the formulated LPP.

Let No. of Wine glasses manufactured be W, Beer glasses be B, Champagne glasses be C and Whiskey glasses be H.

Total Profit = 6 * W + 10 * B + C * 9 + 20 * H

We have to maximize the profit. Hence, we get the objective function as:

Maximize Total Profit P = 6W + 10B + 9H + 20W

Total Molding time required = 4W + 9B + 7H + 10C

Molding time available = 600 minutes

Hence, we get constraint as 4W + 9B + 7H + 10C <= 600

Similarly, we get other constraints as:

1W + 1B + 3H + 40C <= 400.........Constraint for availability of Packaging time

3W + 4B + 2H + 2.5C <=500..........Constraint for availability of Glass

Hence, we get formulation as show below:

Maximize Total Profit P = 6W + 10B + 9H + 20W

4W + 9B + 7H + 10C <= 600

1W + 1B + 3H + 40C <= 400

3W + 4B + 2H + 2.5C <=500

W, B, H, C >= 0.........................Non-negativity constraints as No. of glasses cannot be negative.

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