1.

b.

c.

2. a.

Constraints are:

time: 4x + 12y ≤ 180

lanolin: 60x + 100y ≤ 1800

packing: x + y ≤ 25

(also x ≥ 0 and y ≥ 0)

b. Maximum occurs at x = 17.5 and y = 7.5

c. 18 jars of rosemary and 7 jars of lavender.

3. a. Inequalities are:

x ≥ 0, y ≤ 5

4x+ 3y ≤ 25

2x + 5y ≥ 16

b. Vertices are: A = (0, 3.2), B = (0, 5), C = (2.5, 5) and D = (5.5, 1)

c. 5x + 4y has these values:

A. 12.8

B. 20

C. 32.5

D 31.5

**Therefore the maximum value is 32.5**

4. a. (i) The number of electronic transactions is equal to or greater than the number of paper transactions.

(ii) y ≤ 12

b.

c. Total monthly bank fee, C = 40x + 25 y

d. From the graph:

A | (4, 12) | C = 460 |

B | (12, 12) | C = 780 |

C | (6, 6) | C = 390 |

D | (4, 10) | C = 410 |

So the bank fee is a minimum with 6 paper transactions and 6 electronic transactions.