two bakeries produce three types of cookies, chocolate chip, sugar, and peanut butter. the cookies are produced in batches containing some of each type of cookie. the cooks will not break up a batch, so you must buy an entire batch of cookies if you want any cookies. mrs. betty's bakery produces 3 dozen CC, 4 dozen S, and 1 dozen PB in a batch, and it charges 30 for the cookies produced in a batch. crazy cookies produces 5 dozen CC, 1 dozen S, and 2 dozen PB in a batch, and it charges 35 dollars for the cookies produced in a batch. if a consumer wants t least 100 dozen CC, 35 dozen S and 14 dozen PB, how many batches should be ordered from each bakery in order to minimize costs.

If you buy x batches at Betty's and y batches at Crazy,

minimize 30x+35y subject to
3x+5y >= 100
4x+y >= 35
x+2y >= 14

Looks like minimum cost at x=4.4, y=17.3, so that would be

5 batches at Betty's
18 batches at Crazy

How many batches of cookies can i make with 5lbs of butter if it takes 3/4 of a lb per batch

To determine the optimal number of batches to order from each bakery, we need to compare the costs of ordering from Mrs. Betty's bakery and Crazy Cookies for each type of cookie.

Let's start by calculating the cost per dozen cookies for each bakery:

- Mrs. Betty's Bakery: 30 dollars / 8 dozen cookies = 3.75 dollars per dozen
- Crazy Cookies: 35 dollars / 8 dozen cookies = 4.375 dollars per dozen

Now, let's calculate the minimum number of batches needed to meet the desired quantities for each type of cookie:

- Chocolate Chip (CC): At least 100 dozen required
- Mrs. Betty's Bakery: 100 dozen / 3 dozen per batch = 33.33 batches (round up to 34 batches)
- Crazy Cookies: 100 dozen / 5 dozen per batch = 20 batches
- Choose Crazy Cookies as it requires fewer batches.

- Sugar (S): At least 35 dozen required
- Mrs. Betty's Bakery: 35 dozen / 4 dozen per batch = 8.75 batches (round up to 9 batches)
- Crazy Cookies: 35 dozen / 1 dozen per batch = 35 batches
- Choose Mrs. Betty's Bakery as it requires fewer batches.

- Peanut Butter (PB): At least 14 dozen required
- Mrs. Betty's Bakery: 14 dozen / 1 dozen per batch = 14 batches
- Crazy Cookies: 14 dozen / 2 dozen per batch = 7 batches
- Choose Crazy Cookies as it requires fewer batches.

Therefore, to minimize costs, you should order 20 batches of Chocolate Chip cookies, 9 batches of Sugar cookies from Mrs. Betty's Bakery, and 7 batches of Peanut Butter cookies from Crazy Cookies.