Answer to Question #254243 in Operations Research for Boomie

Question

A margarine factory has two machines capable of pressing sunflower seeds to oil. Together the two machines need to produce at least 900 litres of oil per day. Machine A always produce at least twice as much oil as machine B. The other processes involved in the factory determine that the two machines should produce at most 1500 litres of oil per day. The cost of producing a litre of oil from machine A and B is in the ratio 3:2. Using the graphical method determine how much oil should each machine produce at minimum cost and determine the minimum cost if the cost of producing a litre of oil from machine B is N$1-00.

(Use the graph paper. Scale: 1 cm=250 units on both axes)

Answer 1

Let machine A should produce $x$ litres of oil per day, machine B should produce $y$ litres of oil per day.

$$x+y\geq900$$

$$x\geq2y$$

$$x+y\leq1500$$

Minimize $P=1.5x+y$

Subject to

$$x+y\geq900$$

$$x\geq2y$$

$$x+y\leq1500$$

$$x\geq0, y\geq0$$

Point $A(600, 300)$

$$P(600, 300)=1.5(600)+300=1200$$

Point $B(1000, 500)$

$$P(1000, 500)=1.5(1000)+500=2000$$

Point $C(1500, 0)$

$$P(1500, 0)=1.5(1500)+0=2250$$

Point $D(900, 0)$

$$P(900, 0)=1.5(900)+00=1350$$

At minimum cost machine A should produce $600$ litres of oil per day, machine B should produce $300$ litres of oil per day.