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Additional Maths Question With a Debatable Answer. watch

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    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 tb) P = 22c 70tc) P = 4c td) P = c 4tIt was argued that B was correct, although it was also argued that both C and D were correct. Which is truly right?

    Yes it's inaccurately worded. If you were were really trying to maximize the total number of tables and chairs you'd just buy all chairs. In reality he wants to buy as many tables as possible, subject to the constraints on cost and chairs.
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Updated: February 28, 2018

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