A manufacturer has employed 5 skilled men and 10 semi-skilled men and makes two models A and B of an article. The making of one item of model A requires 2 hours work by a skilled man and 2 hours work by a semi-skilled man. One item of model B requires 1 hour by a skilled man and 3 hours by a semi-skilled man. No man is expected to work more than 8 hours per day. The manufacturer's profit on an item of model A is Rs. 15 and on an item of model B is Rs. 10. How many of items of each model should be made per day in order to maximize daily profit? Formulate the above LPP and solve it graphically and find the
maximum profit.

From the given information, 

Let x articles of model A and y articles of model B be made.

Number of articles cannot be negative.

Therefore, $\mathrm{x}, \mathrm{y}\ge 0$

According to the question, the making of a model A requires 2 hrs. work by a skilled man and the model B requires 1 hr by a skilled man

$2\mathrm{x}+\mathrm{y}\le 40$

The making of a model A requires 2 hrs. work by a semi-skilled man model B requires 3 hrs. work by a semi-skilled man.

$2\mathrm{x}+3\mathrm{y}\le 80$

Total profit=Z=15x+10y which is to be maximised

Thus, the mathematical formulation of the given linear programming problem is 

Max Z=15x+10y

subject to 

$$\begin{gathered} 2\mathrm{x}+\mathrm{y}\le 40 \\ 2\mathrm{x}+3\mathrm{y}\le 80 \\ \mathrm{x}\ge 0 \\ \mathrm{y}\ge 0 \end{gathered}$$

Now, the feasible region determined by system constraints, it follows

Notice from the graph the corner points are $\mathrm{A} \left(0, \frac{80}{3}\right), \mathrm{B}(10, 20), \mathrm{C}(20, 0).$

 The values of Z for the obtained points are as follows in table,  

Notice that the maximum value of Z is 350at B(10, 20)

Therefore, the maximum profit is Rs. 350 which obtained when 10 units of deluxe model and  20 units of ordinary model is produced.

Which are required answers.