Question

A plant that produces margarine has two machines that can press canola seed into

an oil. The two machines together must produce at least 900 litres of oil per day.

Machine A produces at least twice as much oil as machine B at all times. The other

processes involved in the factory stipulate that the two machines can produce a

maximum of 1500 litres of oil per day. The production cost per litre of oil of the two machines A and B is in the ratio 2: 3.

Determine the number of litres of oil that is pressed by the respective machines if the

cost is a maximum and the cost is a minimum.

Answer 1

Solution:

Let the number of litres produced by machine A and machine B be $x$ and $y$ respectively.

Subject to constraints:

$x+y\ge900$

$x\ge2y$

$x+y\le1500 \\ x,y\ge0$

Cost function: $Z=2x+3y$

Plotting these inequations:

ABCD is the feasbile reason.

A(600, 300), B(1000, 500), C(1500, 0), D(900, 0)

Z at A = 2(600)+3(300) = 1200 + 900 = 2100

Z at B = 2(1000)+3(500) = 2000 + 1500 = 3500 ---> Maximum

Z at C = 2(1500)+3(0) = 3000 + 0 = 3000

Z at D = 2(900)+3(0) = 1800 + 0 = 1800 ---> Minimum

So, maximum cost is 3500 at (1000, 500) and minimum is 1800 at (900, 0).