Homework Help: algebra

Posted by James on Wednesday, October 31, 2012 at 3:56am.

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.

algebra - Steve, Wednesday, October 31, 2012 at 11:25am
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

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