Maths - Ordinary P2 Q11

CaoimH_in

Linear Programming.. can someone please explain how I go about this? only question im stuck on

Futurism

Is there a specific section/problem you have or just the whole thing?

Pala!

I also stuck on a part of this.

Just the first part, usually A.

Write down Three Inequalities that together define the shaded region.

I can't do that or find the equation if asked. Can someone explain that.

I can do (b) though.

CaoimH_in

Q1 (b) A small restaurant offers two set lunch menus each day: a fish menu and a meat menu.
The fish menu costs €12 to prepare and the meat menu costs €18 to prepare.
The total preparation costs must not exceed €720.
The restaurant can cater for at most 50 people each lunchtime.

(i) Taking x as the number of fish menus ordered and y as the number of meat menus
ordered, write down two inequalities in x and y and illustrate these on graph paper.

(ii) The price of a fish menu is €25 and the price of a meat menu is €30. How many
of each type would need to be ordered each day to maximise income?

(iii) Show that the maximum income does not give the maximum profit.

Q2

(a) (i) Does the point (18, −15) satisfy the inequality 3x + 5y +11 ≥ 0 ?
Justify your answer.

(ii) The equation of the line K is

x + 2y + 4 = 0.
Write down the inequality which defines

the shaded half-plane in the diagram.

Diagram here
http://www.examinations.ie/archive/exampapers/2008/LC003GLP200EV.pdf
on page 8.

Just go through it and add you reasoning like too

SCD

The trick is. When they ask you to show on the diagram what side it is. Dont use arrows. Shade it in. Because even if you're wrong you get full marks. It's because you could have either meant to include or not include that side

mink_man

just when you have the inequalitys thats define the shaded region, do you have to sub in, say, (0,0) to show which way its going even though its obvious which way its going!

errlloyd

A small restaurant offers two set lunch menus each day: a fish menu and a meat menu.
The fish menu costs €12 to prepare and the meat menu costs €18 to prepare.
The total preparation costs must not exceed €720.
The restaurant can cater for at most 50 people each lunchtime.

Ok so here is your question.

You need to define the limitations as such

So you can't spend more than 720, and you can make meals using 12 and 18, so make one x and one y...

18x + 12y </= 720
(cancel this down)
3x + 2y </= 20

The other limitation is the amount of people (each person eats one meal)

so that's simple

x + y </= 50

So your inequalities are

3x + 2y </= 20
x + y </= 50

To graph them simple put the x and y values equal to zero and take away the less than sign, just use and equal to.

So you would get x = 50 (when why is 0)

So put one end of your line at 50 on the y axis

then you get y = 50 (when x is 0)

So put the other end on the x axis at 50


Do the same (Albeit slightly more complex) thing for the other inequality.



Then get the point where the two lines cross (put the ineqaulties equal to each other)

Once you have that point get your 4 apexs (4 corners) of the quadrilateral and sub in the values of the meals.

So 50,0
0,50
0,0
(and lets say) 20,30


sub in the money made on each meal, and find out which apex is the most profitable.

And boom... Your done.

errlloyd

Oh sorry its a little more complex (very little) you're going to have to sub both the cost and the sell price, and do simple subtraction to get the part c. But its dead easy, once you get your head around it.

Btw for this

(a) (i)
Does the point (18, −15) satisfy the inequality 3x + 5y +11 ≥ 0 ?
Justify your answer.

Just sub the points into the inequaility so...

18(3) + 5(-15) + 11 ≥ 0
72 - 75 + 11 ≥ 0
8 ≥ 0

So its true, it does satisfy the inequality.