Question: 1. A firm is planning to offer one of four new products, P1 - P4, and wishes to maximize profit, minimize risk, whilst increasing market share. If a weight of 50% is assigned to profit potential, 20% to profitability risk, and 30% to market share, identify the product that would be best for the firm to introduce.

2. The expected profit for 3 marketing strategies, M1 - M3, and 3 potential levels of sales, L1 - L3, is as follows:

i) Graph the level of sales according to the Hurwicz rule for all values of α.

ii) Which marketing strategy would you use if you were neither pessimistic nor optimistic about the future (i.e. α ~ 0.5)?

3. An office building and its equipment are insured for $50,000,000. The present annual insurance premium is $25 per $1000 of coverage. A sprinkler system with an estimated life of 25 years and no salvage value can be installed for $250,000. Annual maintenance and operating cost is estimated to be $10,000. The premium will be reduced to $15 per $1000 coverage if the sprinkler system is installed.

i) Find the rate of return if the sprinkler system is installed.

ii) If interest is fixed at 4 %, find the payout period for the sprinkler system.

4. A chemical company owns two plants, I and II, that produce identical product. The annual capacity of plant I is 500,000 litres while that of B is 375,000 litres. The annual fixed cost of plant I is $250,000 per year and the variable cost $2.50 per litre. The corresponding values for plant II are $200,000 and $3.00 per litre, respectively. Plant I is being operated at 45% capacity and plant II is being operated at 35% of capacity.

i) What would be the total cost to the company and cost per litre if all production were transferred to Plant I (whilst retaining but not operating Plant II)?

ii) If the total demand for product is 1,000,000 litres per year, what is the optimum capacity at which Plants I and II should be operated (i.e. to minimise production costs).

5. A used automobile can be purchased by a student to provide transportation to and from university for $25,000 as-is (i.e. without warranty). First year maintenance cost is expected to be $750 and the maintenance costs will increase by $150 per year thereafter. Operation costs for the automobile will be $5,000 for every year the automobile is used, and its salvage or resale value is expected to decrease by 20% per year. What is the economic life of the vehicle if the rate of interest is 5%?

6. The demand for a certain item is 360 units per period. Unsatisfied demand causes a shortage cost of $120 per unit per period. The cost of initiating manufacturing is $1000.00 and the holding cost is $3.00 per unit per period. Production cost is $300.00 per unit and the item may be produced at a rate of 400 units per period. Each item consumes 5 cubic units of warehouse space. The warehouse space reserved for this item is limited to 500 cubic units.

i) Find the minimum-cost procurement quantity and the procurement level under this restriction if the lead time is 5 periods.

ii) What is the cost penalty per period due to the warehouse restriction?

7. Each truck in a fleet of 120 delivery trucks returns to a warehouse for reloading at an average interval of 120 minutes. An average of 30 minutes is required by the driver and one warehouse person to load the next shipment onto the truck. If warehouse personnel are busy loading previous arrivals the driver must wait in a line. Both the time between arrivals and the loading time are distributed exponentially. The cost of waiting in line is $300 per hour per truck, and the total cost per warehouse person is $100 per hour. Find the minimum cost number of warehouse personnel to employ.

8. A group of 30 machines are repaired by a single repair person when they break down. Each machine yields a profit of $15 per hour while running. The mechanic costs the firm $150 per hour, including overheads. At the present time no preventative maintenance is used. It is proposed that one technician be employed to perform certain routine maintenance and adjustment tasks. This will cost $60 per hour but will reduce the service factor from 0.1 to 0.04. What is the economic advantage, or disadvantage, of implementing preventative maintenance?

9. During an 18-day inspection period, the number of defects found in a sample of 500 components are listed in the table, below. Construct a c chart for these data. Does it appear as though there was an assignable cause of variation during the inspection period?

10. Nine activities and eight events are required to execute and complete a construction program. The activities and their completion times in weeks are as follows:

i) Represent the program in the form of an activity-event network and identify the critical path.

ii) Determine the shortest possible time for program completion.