Linear Programming: Bakery Problem
Mathematics

Tutor: None Selected  Time limit: 1 Day 
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 halfdozen of waffles and 3 minutes to make a halfdozen 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?
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.
Considering C(0, 200)
x = 0, y = 200
then, P = 2*0 + 1.5*200 = 0 + 300 = $300
Considering B(160, 120)
x = 160 , y = 120
then, P = 2*160 + 1.5*120 = 320 + 180 = $500
Considering A(250, 0)
x = 250, y = 0
then, P = 2*250 + 1.5*0 = 500 + 0 = $500
So there are two possible ways to maximize profit
i) Number of muffins = 160 and Number of waffles = 120
ii) Number of muffins = 250 and Number of waffles = 0
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