Answer to Question #254243 in Operations Research for Boomie

Question #254243

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)


1
Expert's answer
2021-10-21T12:29:40-0400

Let machine A should produce xx litres of oil per day, machine B should produce yy litres of oil per day.


x+y900x+y\geq900

x2yx\geq2y

x+y1500x+y\leq1500

Minimize P=1.5x+yP=1.5x+y

Subject to


x+y900x+y\geq900

x2yx\geq2y

x+y1500x+y\leq1500

x0,y0x\geq0, y\geq0


Point A(600,300)A(600, 300)


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

Point B(1000,500)B(1000, 500)


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

Point C(1500,0)C(1500, 0)


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

Point D(900,0)D(900, 0)


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


At minimum cost machine A should produce 600600 litres of oil per day, machine B should produce 300300 litres of oil per day.


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