Description
Bakery has bought 250 pounds of muffin dough. They want to make waffles or muffins in half dozen packs out of it. Half a dozen of muffins requires 1 lb of dough and a pack of waffles uses 3/4 lb of dough. It take bakers 6 minutes to make a half-dozen of waffles and 3 minutes to make a half-dozen of muffins. Their profit will be $1.50 on each pack of waffles and $2.00 on each pack of muffins. How many of each should they make to maximize profit, if they have just 20 hours to do everything?
Explanation & Answer
Let the number of packs of muffins be x
and the number of packs of waffles be y.
Amount of dough required for a pack of muffins = 1 lb
Amount of dough required for a pack of waffles = 3/4 lb
Total amount of dough available = 250 pounds = 250 lbSo, the inequality can be written as
Time taken to make a pack of muffins = 3 min
Time taken to make a pack of waffles = 6 min
Total time available = 20 hours = 20*60 min = 1200 min
So, the inequality can be written as
Profit for a pack of muffins = $2
Profit for a pack of waffles = $1.5
Total profit, P = 2x + 1.5yP has to be maximised.
So, the constraints to be considered are
Its vertices can be used to find the maximum profit.
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