Question

Q2: A small manufacturer employs 5 skilled men and 10 semi-skilled men and makes an article in 2 qualities, a deluxe model and an ordinary model. The making of a deluxe model requires 2 hours work by a skilled man and 2 hours work by a semi-skilled man. The ordinary model requires 1 hour work by a skilled man and 3 hours work by a semi-skilled man. By union rules no man can work more than 8 hours per day. The manufacturer’s clear profit of the deluxe model is $ 10 and of the ordinary model is $8. Formulate the model of the problem.

Solution:

Answer 1

We tabulate the given data as shown below:

As seen from above, the number of available hours are calculated as:

Skilled hours = No. of Skilled labour available * Hours per day = 5 * 8 = 40 hours

Semi-skilled hours = No. of Semi-skilled labour available * Hours per day = 10 * 8 = 80 hours

Based on the above, let the number of Deluxe models be D and No. of Ordinary Models be N.

Hence, Total Profit = 10 * D + 8 * N

We have to maximize the profit

Hence, we get the objective function as:

Maximize Profit P = 10D + 8N

Total Number of skilled labor hours required based on articles = 2 * D + 1 * N

Skilled hours available = 40

Hence, we get constraint as:

2D + 1N <= 40

Similarly, for semi-skilled hours,

2D + 3N <= 80

Hence, we get formulation as:

Maximize Profit P = 10D + 8N

Subject to Constraints

2D + 1N <= 40

2D + 3N <= 80

D, N >= 0................Non-negativity constraint since no. of articles cannot be negative

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