A chef is going to use a mixture of two brands of Italian dressing. The first brand contains \( 9 \% \) vinegar, and the second brand contains \( 14 \% \) vinegar. The chef wants to make \( 250 \) milliliters of a dressing that is \( 12 \% \) vinegar. How much of each brand should she use?
First brand:
Second brand:
22.5
35
Determine the following limits. If infinite, specify \( \infty \) or \( - \infty \) . If an answer does not exist, explain why. (NO POINTS WILL BE GIVEN IF A TABLE OF VALUES IS USED) b. \( \lim _ { x \rightarrow 1 ^ { + } } [ \frac { x } { x - 1 } + \frac { 1 } { \ln ( x ) } ]\)
9. A board game company models the profit on its latest board game using the quadratic relation
\( P = - 2 x ^ { 2 } + 28 x - 90 , \) where \( x \) is the number of games it produces in hundred thousands and \( P \) is the profit in millions of dollars.
a) What are the break-even points for the company?
b) What is the maximum profit that the company can earn?
