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August 22, 2014

Homework Help: math

Posted by Berry on Monday, September 24, 2007 at 12:21am.

Mr. Balk and Mr. Sullivan have created their own cookie factory. In their factory, they bake two and only two types of cookies: the Balkster and the Sullivander. The Balkster cookie requires 1 pound of cookie dough per dozen while the Sullivander requires 0.7 pounds of cookie dough per dozen along with 0.4 pounds of icing. Being math geniuses they also know that the Balkster takes 0.1 hours of preparation time while the Sullivander takes 0.15 hours. Since the cookies are a hot commodity, they know that no matter how many cookies they make, they will sell all of them.

The two men want to become rich (that's why they quit being teachers). Thus, they need to decide how many dozens of each cookie they should make for their grand opening. Their decision rests upon three limiting factors:
The ingredients they have on hand-they have 110 pounds of cookie dough and 32 pounds of icing
The amount of oven space available---they have room to bake a total of 140 dozen cookies for the grand opening
The amount of preparation time available---together they have 15 hours for cookie preparation

Looking within the money, the Balkster cookies cost $4.50 a dozen, but will be sold at $6.00 a dozen. The Sullivander cost $5.00 a dozen while being sold for $7.00 a dozen.

Question: How many dozens of each kind of cookie should Mr. Balk and Mr.
Sullivan make so that their profit is as high as possible?

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