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?

Answer and Explanation:

The number of packets of waffles is W

and the number of muffins are M

The weight of dough is 250 pound and a pack of muffins requires 1 lb of dough whereas a pack of waffles uses 3/4 lb of dough.

3:4W+M≤250

Multiplying both sides by 4

3W+4M≤1000

It takes bakers 6 minutes to make a packer of waffles and 3 minutes to make a pack of muffins, the total time available is 20 hours or 1200 minutes.

3M+6M≤1200

Minus the initial equation from the new equation:

(3M+6M≤1200) - (3W+4M≤1000)

2M≤200

Dividing equation by 2

M≤100

For M≤100

3W+4M≤1000

3W≤1000-4M

For the Maximum values of M

the least value of W is obtained

3W≥1000-4*100

3W≥600

Dividing the equation by 3

W≥300

For maximum profit, the number of waffles and muffins is taken as 300 and 100 respectively:

1.5∗300+2∗100

=650