(Diet problem) A dietician has to develop a special diet using two foods `P` and `Q`. Each packet (containing `30g`) of food `P` contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food `Q` contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of calciums atleast 460 units of iron and at most 300 units of cholesterol. How many packets of each food should be used to minimise the amount of vitamin A in the diet? What is the minimum amount of vitamin A? How many packets of each food should be used to maximise the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?

Answer

(a) 150 units
(b) 40 packets of food P and 15 packets of food Q; Max.amount of vitamin = 285 units.