A SMALL MANUFACTURER HAS EMPLOYED 5 SKILLED N 10 SEMI SKILLED MEN AND MAKES AN ARTICLE IN 2 QUALITIES , - Maths - Linear Programming

Question

A SMALL MANUFACTURER HAS EMPLOYED 5 SKILLED N 10 SEMI SKILLED
MEN AND MAKES AN ARTICLE IN 2 QUALITIES , A DELUXE MODEL AND AN
ORDINARY MODEL THE MAKING OF A DELUX MODEL REQUIRES 2 HR OF WORK BY
A SKILLED LABOUR N 2H OF WORK OF SEMI SKLLED MAN THE ORDINARY MODL
REQUIRES 1H BY SKILLED N 3 H BY SEMI SKILLED ACCORDING TO UNION
RULE NO MAN MAY WORK FOR MORE THAN 8H PER DAY THE MANUFACTURER
GAINS RS15ON DELUX N RS 10 ON ORDINARY IN ORDER TO MAXIMISE PROFIT
HOW MANY OF EACH TYPE SHOULD BE MADE

Anuradha Sharma · Accepted Answer

Let the company produce x deluxe model and y ordinary model
article
Hence, the total time spent by 5 skilled men = 2x+y and it
should be less than 8hours/person
Hence, 2x+y ≤40 (1)
Also, the total time spent by 10 semi-skilled men = 2x+3y and
it should be less than 8hours/person
Hence, 2x+3y ≤80 (2)
Also, ≥x0 (3) and y≥0 (4)
Profit = 15x+10y

We need to maximise profit given the constraints So, for that
draw all the 4 lines on the graph and check the common area, you
will form a hexagon OABC with A(0,80/3); B(10,20); C(20,0);
O(0,0)
Since the feasible region is a bound region, we can check the
profit function at all the vertices to find the point of
maxima
At point A: 15(0)+10(80/3) = 800/3
At point B: 15(10)+10(20) = 350
At point C: 15(20)+10(0) = 300
At point 0: 15(0)+10(0) = 0
So, the maxima lies at point C with x =10and y = 20 and the
maximum profit = Rs 350