**Solve the following questions. **

1. Cedar Point amusement park management is preparing the park’s annual promotional plan for the coming season. Several advertising alternatives exist: newspaper, television, radio, and displays at recreational shows. The information below shows the characteristics associated with each of the advertising alternatives, as well as the maximum number of placements available in each medium. Given an advertising budget of $125,000, how many placements should be made in each medium to maximize total audience exposure? Formulate this as a linear programming problem to be solved using QM.

Type

Cost

Maximum number

Exposure (1000s)

Newspaper

750

50

40

Television

1100

25

60

Radio

325

25

22.5

Shows

75

1.5

5

2. A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $120, while the profit per chair is $80. Currently, each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. To keep a balance, the number of chairs produced should be at least twice the number of tables. Also, the number of chairs cannot exceed six times the number of tables. How many tables and chairs should the furniture manufacturer produce to maximize profit?

3. East Valve Distributors distributes industrial valves and control devices. The Eastern control device has an annual demand of 9,000 units and sells for $90 per unit. The cost of ordering is $150 per order and the average carrying cost per unit per year is $0.85. Determine the economic order quantity.

4. Furniture Manufacturers Inc., uses 10,000 loads of lumber per year. A load of lumber costs $250 and the carrying cost is 10 percent of the unit cost. The cost to order is $100 per order and the lead-time is three working days. Assuming 100 working days, determine:

(a) the economic order quantity.

(b) the reorder point.

(c) number of orders per year.

(d) working days between orders.

5. Demand for local newspapers in King County during weekdays is normally distributed with a mean of 500 and standard deviation of 100. The marginal loss per paper is $0.20 and marginal profit is $0.80. How many newspapers should the local publisher produce each day?

6. Consider the material structure tree for item A below. Assume 15 units of A are needed.

(a) How many units of B are needed?

(b) How many units of C are needed?

(c) How many units of D are needed?

(d) How many units of E are needed?