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?
Question 2 [

- The graph of this linear programming question is presented in the first attached image to this solution.

i) The maximum number of guests that can attend the wedding = 150 guests

ii) Bride can invite 50 guests and the groom can invite 100 guests to maximize the available resources.

Explanation:

Let x represent the number of guests that the bride invites.

Let y represent the number of guests that the groom invites.

- The bride can invite at most 60 guests

x ≤ 60

- 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 ≤ 30,000

- 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 ≤ 500

- 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 ≤ 60

300x + 150y ≤ 30,000

4x + 3y ≤ 500

x > 0

y > 0

The graph of this linear programming question is presented in the first attached image to this solution.

The second attached image to this solution shows each of the graphs plotted on the linear programming graph and the representative colours to recognize each of them.

i) From the acceptable region of values, we have the pairs. This is shown on the third attached image to this solution.

(60, 80)

(50, 100)

(0, 200)

(0, 166.67)

(60, 86.67)

The most correct pairs that satisfy all the conditions include

(60, 80), sum of guests In this case = 140

(50, 100), sum of guests In this case = 150

(60, 86.67), sum of guests In this case = 146.67

Of the 3 possible answers, the maximum number of guests is 150.

ii) From the most optimal solution, (50, 100), the bride can invite 50 guests and the groom can invite 100 guests to maximize the available resources.

Hope this Helps!!!