Answer to Question #254244 in Operations Research for Boomie

Question

As part of a campaign to promote its Summer Annual Clearance Sale, Cassy clothing cc. decided to buy television advertising time on Etu television. Their television advertising budget was N$102 000-00. Morning time costs N$3000-00 per minute, afternoon time costs N$1000-00 per minute, and evening (prime) time costs N$12 000-00 per minute. Because of previous commitments, Etu television could not offer Cassy clothing more than 6 minutes of prime time and a total of 25 minutes of advertising time over the two weeks in which the commercials run in the morning would be seen by 200 000 people, those run in the afternoon would be seen by 100 000 people and those run in the evening would be seen by 600 000 people. How much morning, afternoon, and evening advertising time should Cassy clothing buy to maximize exposure of its products?

Answer 1

Let Cassy clothing should buy $x$ minutes of morning time, $y$ minutes of afternoon time and $z$ minutes of evening (prime) time

$$3000x+1000y+12000z\leq102000$$

$$x+y+z\leq25$$

$$x\geq0, y\geq0, 0\leq z \leq 6$$

Maximize $P=200000x+100000y+600000z$

Subject to

$$3x+y+12z\leq102$$

$$x+y+z\leq25$$

$$x\geq0, y\geq0, 0\leq z \leq 6$$

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.