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

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explanation:

rational decision making is a multi-step process for making choices between alternatives. the process of rational decision making favors logic, objectivity, and analysis over subjectivity and insight. the word “rational” in this context does not mean sane or clear-headed as it does in the colloquial sense.

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