Question

If a factory manufactures 964 nut-bolts every day, what would be the number of nut-bolts manufactured in 30 days?

Estimate by rounding off the number of nut-bolts manufactured per day to the nearest thousand.

Answer 1

Answer:

Let x be the no. of nuts & y be the bolts.

We have to maximize x & y if the factory worked at capacity of 12hours per day.

Clearly, x≥y,y≥0

Since we have only 12 hours of machine, we will use the following constraints:-

x+3y≤12

3x+y≤12

The profit of nuts is Rs.17.5 and bolts is Rs. 7 .

We need to maximize 17.5x+7y

We can see that the feasible region is bounded and in the first quadrant.

On solving the equations, x+3y=12 and 3x+y=12, we get x=3 and y=3.

Therefore, feasible points are (0,0);(0,4);(3,3);(4,4)

Values of z are(z=17.5x+7y)

The maximum profit =73.5 which is when 3 packets each of nuts & bolts are produced.