Quiz 10

Date: MATH 1090-4 - Fall 2003

Note: Unless stated otherwise, answers without justification receive no credit. Please, show your work!

1. Read the following problem, but do not solve it!

   A privately owned lake contains two types of game fish, bass and trout. The owner provides two types of food, A and B, for these fish. Bass require $2$ units of food A and $4$ units of food B, and trout require $5$ units of food A and $2$ units of food B. If the owner has $800$ units of each food, find the maximum number of fish that the lake can support.

   1. What variables would you use to describe the problem?
   2. Write the feasible region to be used to solve the problem (that is, write down the inequalities but do not graph!).
   3. Write the function that you want to maximize or minimize in this problem.
   4. Do you want to maximize or minimize the function that you wrote in the previous item?

2. Consider $f(x,y)=2x-y$ and the feasible region

   $$\begin{cases}x\leq 10\\ y\geq 0\\ 2x-3y\geq -4\\ 2x+y\geq 12. \end{cases}$$

   
   
   1. Sketch the graph of the feasible region showing clearly the coordinates of each corner.
   2. Find the maximum and minimum values of $f(x,y)$ over the feasible region. If any of these values does not exist, explain why.