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?

250 batches of muffins and 0 waffles.

Step-by-step explanation:

-1

If we denote the number of batches of muffins as "a" and the number of batches of waffles as "b," we are then supposed to maximize the profit function

P = 2a + 1.5b

subject to the following constraints: a>=0, b>=0, a + (3/4)b <= 250, and 3a + 6b <= 1200. The third constraint can be rewritten as 4a + 3b <= 1000.

Use the simplex method on these coefficients, and you should find the maximum profit to be $500 when a = 250 and b = 0. So, make 250 batches of muffins, no waffles.

You use up all the dough, have 450 minutes left, and have $500 profit, the maximum amount.

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.