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# Interesting Additional Maths Problem - Linear Programming Problem watch

1. In one of my Additional Maths classes after school the other day, an interesting question popped up on our end of unit test, specifically, section 6 of the OCR Ad Maths book.

It was regarding the Objective Function of our problem, yet our class had mixed opinions on what the answer actually was, which is surprising considering the average intelligence of those in the class.

It goes as follows:

A Linear Programming problem is as follows:
The cost of a chair is £22 and the cost of a table is £70. A cafe owner wishes to purchase as many chairs and tables as possible. There is a maximum of £300 available for the purchase. He must buy at least four times as many chairs as tables.

Let the number of chairs bought be 'c' and the number of tables be 't' (You may assume that c ≥ 0 and t ≥ 0.) Two constraint of the problem are represented algebraically by one of the following sets of inequalities. Which one?

We determined it was 22c + 70t ≤300 and c ≥ 4t. Simple right?

The next part of the question is what stumped us:

In the problem of Question 8, it was stated that the cafe owner wishes to purchase as many chairs and tables as possible. One of the following is the Objective Function. Which one?
a) P = c + t
b) P = 22c + 70t
c) P = 4c + t
d) P = c + 4t

It was argued that B was correct, although it was also argued that both C and D were correct. Which is truly right?
2. (Original post by Spannerr)
In the problem of Question 8, it was stated that the cafe owner wishes to purchase as many chairs and tables as possible. One of the following is the Objective Function. Which one?
a) P = c + t
b) P = 22c + 70t
c) P = 4c + t
d) P = c + 4t

It was argued that B was correct, although it was also argued that both C and D were correct. Which is truly right?
She wishes to maximise the number of tables and chairs, i.e. "c + t". So answer is A.

B is the cost of the tables and chairs.

Edit: The question is rather poorly formulated since as it stands, she'd just buy chairs and no tables. Option D would give a better balance, but it's not what's posed by the question.

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