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1) Sketch the region described by the inequalities.

2. Maximize Z = 4x + y

3. A company has two different locations to assemble three different models of PCs. The table below summarizes the daily production capacity, the minimum number of each type needed, and the daily operating costs for each location. Find the number of days that each location needs to operate to fill the orders at minimum cost.

Location 1 Location 2 Minimum Number

Model 1 60/day 60/day 2400

Model 2 40/day 80/day 2000

Model 3 60/day 40/day 1800

Daily Cost $16,000 $12,000

4. Use the Simplex Method to

Maximize Z = x1 + 4×2 + x3

Subject to x1 + x2 + x3 ≤ 6

x1 – x2 – 2×3 ≤ 2

x1, x2, x3 ≥ 0

5. Use the simplex method to

Maximize Z = 2×1 – 3×2

Subject to x1 + x2 ≥ 5

x1 + 2×2 ≤ 8

x1, x2 ≥ 0

6. Use the Simplex Method to

Minimize Z = 4×1 + x2

Subject to x1 + x2 ≥ 5

x1 + 2×2 ≥ 8

x1, x2 ≥ 0

7. Solve the matrix equation

8. A small airline has 3 flights, A, B, and C, to each of 3 cities in Colorado. The

matrix N represents the number of passengers carried in November, and matrix D

represents the number of passengers carried in December. Write a matrix that shows the total number of passengers carried in these two months.

Denver

Boulder ;

9. A bookstore has 100 dictionaries, 70 cookbooks, and 90 thesauruses in stock, and a second store with 85 dictionaries, 95 cookbooks, and 60 thesauruses in stock. If the value of each dictionary is $28, each cookbook is $22, and each thesaurus is $16, use the matrix operations on a graphing calculator to find the total value of the bookstore’s inventory.

10. On Saturdays, the air freight company must move 23 tons of mail, 16 tons of medical supplies, and 17 tons of freight. This system of equations can be represented by the matrix:

11. If A is the coefficient matrix of the system , determine A-1.