finding the equation out of a word problem

[bigguy252]

the problem with doing my homework is not in the actual calculus part of the work. i just find it hard to extract the problem from the words. any help would be great.

1. the management of a restaurant assigns each waitress between 7 and 15 tables. one waitress finds that when she is assigned seven tables, each table brings in $30 per week in tips. if she is assigned more tables the amount of attention she gives to each table decreases. thus, each table brings in less per week in tips. suppose each additional table causes every table to bring $2 less per week in tips. use calculus to determine how many tables she should be assigned to maximize her weekly earnings from tips. what are her weekly earnings when she is assigned this number of tables? hint try different actual scenarios to construct the function needed.

2. peter potter wants to make 1200 copies of a vase he designed. his kiln has space for at most 24 molds and consumes $6 worth of electricity every time is fired, it cost $32 to build each mold. if each mold is reusable , how many molds should peter build and use to minimize the combined cost of the molds and the electricity? what is this minimum cost?

thanks for any help you guys

 

[galactus]

1. the management of a restaurant assigns each waitress between 7 and 15 tables. one waitress finds that when she is assigned seven tables, each table brings in $30 per week in tips. if she is assigned more tables the amount of attention she gives to each table decreases. thus, each table brings in less per week in tips. suppose each additional table causes every table to bring $2 less per week in tips. use calculus to determine how many tables she should be assigned to maximize her weekly earnings from tips. what are her weekly earnings when she is assigned this number of tables? hint try different actual scenarios to construct the function needed.

The number of tables times the money brought in per table would be her total intake for the week. Correct?.

Let x = the number of tables added.

\(\displaystyle \L\\E(x)=(7+x)(30-2x)\)

Now, do the differentiating thing, set to 0 and solve for x.

Try the various scenarios. You'll see.

 

[bigguy252]

thanks for the help galactus. does anyone have a clue about that second one :?: