Reddy produces two types of cups (Type 1 and Type 2). A Type 1 cup needs twice as much labour time...

Question

Reddy produces two types of cups (Type 1 and Type 2). A Type 1 cup needs twice as much labour time as a Type 2 cup. If all the available labour time is dedicated to Type 2 cup alone, the company can make a total of 440 Type 2 cups a day. The respective market limits (maximum order) for the two types are 150 and 200 cups per day. The revenue is $6 per Type 1 cup and $4 per Type 2 cup. Let x, y be the number of Type 1 cups and Type 2 cups made per day, respectively. The company plans to maximise its revenue. (1) Formulate the problem as a linear program. (2) Use the graphical solution to determine the optimal solution. (3) If the daily demand limit on the Type 1 cup is decreased to 120, does the optimal solution changed? (4) How much can the market limit increase for Type 2 cup when the optimal solution remains.

Komalavalli · Accepted Answer

Linear Programming model:
the firm produces x of type 1 cups and  y of type 2 cups
Each day clearly
x≥0, y≥0
Objective function 
Let us consider Z as Revenue
Z = 6x+ 4y
Let labor time for type 2 cup is t
2xt+yt ≤440yt
2x+y=440
In the point of sales view
x≤150;y≤200
1.

Reddy produces two types of cups (Type 1 and Type 2). A Type 1 cup needs twice as much labour time as a Type 2 cup. If all the available labour time is dedicated to Type 2 cup alone, the company can...

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