1. Petrochemical Sales: Mexico The following table shows annual petrochemical sales in Mexico by PEMEX, Mexico's national oil company for 2005-2010 (t=0 represents 2005)
| Year t (Year since 2005) |
0 |
1 |
2 |
3 |
4 |
5 |
| Petrochemical Sales s (Billion metric tons) |
3.7 |
3.8 |
4 |
4.1 |
4 |
4.1 |
a. Find s(1), s(4) and s(5).
b. What is the domain of s?
2. A piano manufacturer has a daily fixed cost of $1,200 and a marginal cost of $1,500 per piano.
a. Find the cost C(x) of manufacturing x pianos in one day. Hint: A linear cost function, C(x) = mx + b. Use your function to answer parts b to e.
b. On a given day, what is the cost of manufacturing 3 pianos?
c. What is the cost of manufacturing the 3rd piano that day?
d. What is the cost of manufacturing the 11th piano that day?
e. What is the variable cost? What is the fixed cost? What is the marginal cost?
3. CSUB college newspaper BakeSizzleNews has fixed production costs of $70 per edition and marginal printing and distribution costs of 40 cents per copy. BakeSizzleNews sells for 50 cents per copy.
a. Write down the associated cost, revenue and profit functions.
b. What profit (or loss) results from the sale of 500 copies of the BakeSizzleNews?
c. How many copies should be sold in order to break even?
4. What is the slope of the linear function that passes through (2, 7) and (6, 13)?
5. Find the equation of the specified line passing through (3, 2) with slope -3.
6. Find the equation of the specified line passing through (1, -3) and (5, 2).
7. Find the equation of the specified line passing through (1, 2) and parallel to x - 2y = 2.