Your paint inventory consists of 60 gallons of blue, 40 gallons of red, and 30 gallons of yellow. To make purple paint you mix equals parts of blue and red. To make orange paint you mix equal parts of red and yellow. To make green paint you mix equal parts of blue and yellow. Purple paint sells for $6 a gallon, orange for $20, and green for $9.

There is a fixed disposal charge for every unused gallon. How much of each of purple, orange, and green paint should you mix to maximize profits if the disposal cost is (a) $4 per gallon, and (b) $6 per gallon.

(In reply to Linear maximization (Solution) by Brian Smith)

Something must be wrong. With $4 per gallon disposal, 20 gallons of orange and 60 of green would produce a selling price of $940, which, less the $200 disposal fee would net $740, plus it uses 40 gallons of yellow, which is more than we have.

It is the 60 gallons of orange and 20 of purple, listed for the $6/gallon disposal that's actually the maximum for the $4 disposal, and at $6/gallon disposal, the 60 orange/20 purple would net only $1020, which is less than the $1070 that is indeed the maximum for $6/gallon disposal with the said 70 purple, 10 orange and 50 green.

Posted by Charlie on 2003-05-12 16:10:58