Answer to Question #120137 in Linear Algebra for Peuyehafo

Question

A couple is planning a wedding and they need to decide how many guests on the bride’s side
as well as on the groom’s side to invite. The couple has agreed that the bride can invite at
most 60 guests. Since the bride’s friends and family are very fancy it costs N$300 per guest
on her side while it only costs N$150 per guest on the groom’s side and they have a budget
of N$30000. Each guest on the bride’s side will receive 4 drink tickets and each guest from
the groom’s side will receive 3 drink tickets and no more than 500 drink tickets can be given.
Keeping in mind that both the bride and groom must have guests (neither of them can attend
the wedding without any of their friends or family present).
Draw a graph and use it to answer the following questions:
i. What is the maximum number of guests that can attend the wedding?
ii. How many guests will the bride and the groom each invite?

Answer 1

Let x be the number of guests of the bride.

Let y the number of guests of the groom.

The bride can invite at most 60 guests:

$x\le60;$

I costs N$300 per guest on her side while it only costs N$150 per guest on the groom’s side and they have a budget of N$30000.

$300x+150y\ge30000;$ /150

$2x+y\ge200;$

$y\ge200-2x;$

Each guest on the bride’s side will receive 4 drink tickets and each guest from the groom’s side will receive 3 drink tickets and no more than 500 drink tickets can be given.

$4x+3y\le500;$

$3y\le500-4x;$

$y\le\dfrac{500-4x}{3};$

Keeping in mind that both the bride and groom must have guests (neither of them can attend the wedding without any of their friends or family present).

$x>0;$

$y>0;$

This is a linear programming question. Combining all the equations as ontained above

$x\le60;$

$y\ge200-2x;$

$y\le\dfrac{500-4x}{3};$

$x>0;$

$y>0;$

We build graphs of inequalities

i)Maximum number of guests=150;

ii)The bride has 50 guests and the groom has 100 guests .

Answer: i)Maximum number of guests=150;

ii)The bride has 50 guests and the groom has 100 guests.