Take Home Quiz 2 Math 141 Print Name________________________________

Sections 1.5-2.3

Help is legal

1. In the table, x is the quantity, S(x)= the supply price, the price producers want if x units are produced, , and D(x)= the demand price, is the price consumers will pay for all x units to be sold.

x | 40 90 120 220 300

S(x)| 79 86 96 115 130

D(x)| 180 164 150 126 100

a) Find the least squares line for the supply price and also for the demand price. Round each slope to the nearest tenth and each y-intercept to the nearest whole number.

b) Put each equation into general form. Write the augmented matrix for this system. Reduce the matrix using row operations. Find the equilibrium point.

2. Answer a, b, and c for the following. A person will put 30% of his investment into a stock fund that earns a 9% annual rate of return. He will put 20% in precious metals currently growing at 40% and the remainder into bond funds earning 3%. His goal is to have $4000 of interest income. How much should he put into each investment?

a) Define variables clearly.

b) Write 3 equations in general form using the given information. One of these should be the equation for the statement about interest.

c) Solve the system in the calculator using rref and answer the question in the paragraph.

d) Write a true ratio statement relating the amount in the metals to the amount in the stock fund.

Write a true ratio statement relating the amount in bonds to the amount in stocks.

For each, write the word statement and the equation.

3. Given the system of equations in x and y :

a) find the value of k so that the system has no solution.

b) Could you choose k so the system had infinitely many solutions? If so, give k. If not, why not?

4. Write the system as an augmented matrix and solve it showing and labeling all row operations as done in class. Check your answer using rref. It works out nicely if you use the standard procedure outlined in class and do not swap rows.

3.