Algebra · Optimization · Linear inequalities · Word problems · Linear programming
Ali-Baba is standing in a cave full of gold and diamonds. A kilogram of gold is worth \(20\) dinars and a kilogram of diamonds is worth \(60\) dinars. He has a single chest with him. Filled with gold, the chest weighs \(200\) kg; filled with diamonds, it weighs \(40\) kg. The empty chest weighs nothing worth counting. Ali-Baba can carry away at most \(100\) kg. How much gold and how many kilograms of diamonds should he take so that the load he carries out is worth as much as possible?
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Serbian Republic Competition (Republicko takmicenje) 1996, high school grade I, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source