6 Ian the chef is to make vegetable stew and vegetable soup for distribution to a small chain of vegetarian restaurants. The recipes for both of these require carrots, beans and tomatoes. 10 litres of stew requires 1.5 kg of carrots, 1 kg of beans and 1.5 kg of tomatoes.
10 litres of soup requires 1 kg of carrots, 0.75 kg of beans and 1.5 kg of tomatoes. Ian has available 100 kg of carrots, 70 kg of beans and 110 kg of tomatoes.

1. Identify appropriate variables and write down three inequalities corresponding to the availabilities of carrots, beans and tomatoes.
2. Graph your inequalities and identify the region corresponding to feasible production plans. The profit on a litre of stew is \(\pounds 5\), and the profit on a litre of soup is \(\pounds 4\).
3. Find the most profitable production plan, showing your working. Give the maximum profit. Ian can buy in extra tomatoes at \(\pounds 2.50\) per kg .
4. What extra quantity of tomatoes should Ian buy? How much extra profit would be generated by the extra expenditure? \section*{END OF QUESTION PAPER} \section*{OCR}