Question #1

A woman has $42,000 to invest. She has decided to invest all of it by purchasing some shares of stock in each of three companiesa fast-food chain that sells for $40 per share and has an expected growth of 11.5% per year, a software company that sells for $20 per share and has an expected growth of 15% per year, and a pharmaceutical company that sells for $70 per share and has an expected growth of 10% per year. She plans to buy twice as many shares of stock in the fast-food chain as in the pharmaceutical company. If her goal is 12% growth per year, how many shares of each stock should she buy?

fast-food chain----------------

software company--------------

pharmaceutical company-----------

Question #2

A laboratory technician wants to purchase two different feeds, A and B, for its animals. The following table summarizes the nutritional contents of the feeds, the required amounts of each ingredient, and the cost of each type of feed.

	Feed A	Feed B	Required
Carbohydrates	1 Unit/lb	4 Units/lb	40 Units
Protein	2 Units/lb	1 Unit/lb	80 Units
Cost	11/lb	13/lb

How many pounds of each type of feed should the laboratory technician buy to satisfy its needs at minimum cost (in $)?

Feed A------ lb

Feed B------- lb

minimum cost---------$

Question #3

Solve the system of equations.

5x+3y	=	16
3x5y	=	30

(x,y) = ( )

Question #4

This problem involves mixed constraints. Solve it with the simplex method. Assume that all variables are nonnegative.Maximize

f=5x+7y,

subject to the following.

2x	+	5y		37
5x		y		34
x	+	2y		4

The maximum value of the objective function is---------- which occurs at

(x,y) = ( )

.