What will be the maximum profit he can achieve??read the details?

An automobile manufacturing makes auto-mobiles and trucks in a factory that is divided into two shops. Shop A, which performs the basic assembly operation must work 5man-days on each truck but only 2-man-days on each automobile. Shop B, which performs finishing operation must work 3-man-days for each truck and 3-man-days for each automobile that it produces. Because of man and machine limitations Shop A has 180 man-days for week available while shop B has 135 man-days for week. If the manufacturer makes a profit of $300/- on each truck and $200/- on each automobile. What will be the maximum profit he can achieve in a week by producing a combination of trucks and automobiles?

In such questions, you must make a graph and try to find the main points in the feasibility region.

The feasibility region is defined by the constraints… you have

Let number of trucks = t, autos = a

Then

5t + 2a <= 180
3t + 3a <= 135

And u have to maximize 300t + 200a

Now plot the equations 1 and and check the feasibility region and then take points at the edges of the region.

The region u will see will have 4 points (t,a) as (0,0), (0,45), (35,0) and (30,15)

Check the profit at each point and you get
max profit at t = 30 and autos = 15

So u get the profit as:

30x300 + 15x200 = $ 12000

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