Question

An automobile paint manufacturer produces two types of product, Paint X of standard quality and
Paint Y of high quality. There are two components required in making these products: the filler and
the special pigment. Paint X requires 2 units of filler and 3 units of special pigment for each unit
made, and is sold at a profit RM 1.00 per unit. Paint Y requires 4 units of filler and 2 units of special
pigment for each unit made, and is sold at a profit of RM 1.50 per unit. The factory has stocks of 12
units of filler and 10 units of special pigment.
Formulate the above problem as a linear programming problem to maximize the profit and solve it
with graphical method.

Answer 1

Corner point are (0,0),(0,3),(2,2),(3.333,0)

Z=x+1.5y

At point (0,0), the value of z=0+1.5*0=0

At point (0,3), the value of z=0+1.5*3=4.5

At point (2,2), the value of z=2+1.5*2=5

At point (3.333,0), the value of z=3.333+1.5*0=3.333

So, the maximum value of Z is 5 at (2,2)

Solution:

x=2

y=2

maximum value is =5