Navigation Panel: Up | Forward | Graphical Version | PostScript version | SIMMER Home Page | Fields Institute Home | U of T Math Network Home

SIMMER

October 1997 Presentation Topic (continued)

Problems

Question 1. A craftsman can make an ordinary widget in 15 minutes using 10 m of wire and sell it at a profit of \$10. A deluxe widget takes 20 minutes to make, uses 5 m of wire and brings a profit of \$15. The supply of wire is limited to 200 m per day and 8 hours are available for work.

How many widgets of each kind should the craftsman make each day to maximize profit?

Question 2. A distributor keeps 15 cans of paint in Oshawa and 25 cans in Oakville. Orders come in for 23 cans to Toronto and 17 cans to Hamilton. Shipping costs per can are given in the table below:

```
Toronto         Hamilton

Oshawa            \$1              \$3
Oakville          \$2              \$1
```
Find the cheapest shipping schedule.

Question 3. An oil company requires a fleet of tankers for shipping crude and product between six ports. Four routes must be served daily as follows:

```
Route#     From             To        No. ships needed per day

1          Dhahran          New York                3
2          Marseilles       Istanbul                2
3          Naples           Bombay                  1
4          New York         Marseilles              1
```
Assume all tankers are identical. The travel time table between ports is shown below. Assume travel time is independent of direction.
```
Na.   Ma.   Is.   NY.   Dh.   Bo.

Naples               1     2    14     7     7
Marseilles                 3    13     8     8
Istanbul                        15     5     5
New York                              17    20
Dhahran                                      3
```
One day must be added to each end of any route where cargo is carried for loading and unloading. You may find that the solution requires some routes to be travelled empty.

What is the smallest fleet that will do the job? Mark on a sketch where the ships should be located at a typical instant of time.

Question 4. Boatco must determine how many how many boats to produce during each of the coming four quarters (3 month periods). The demand is forecast as 40, 60, 75, and 25 during the next 1st to 4th quarters resp. The number to be produced is decided at the beginning of each quarter. Up to 40 boats can be produced in any quarter without overtime at a cost of \$400 per boat. Beyond 40 boats overtime costs drive up the cost to \$450 per boat. Any boats unsold at the end of a quarter incur a storage and handling cost of \$20 each. Devise a production schedule to minimize the total cost of meeting the demand.

Question 5. Machinco has four machines and four jobs to be completed. Each machine must be assigned to complete one job and each assignment incurs a set-up time. The set-up times are shown below. Find the assignment which minimizes total setup time.

```
Job 1  Job 2  Job 3  Job 4

Machine 1       14     15      8      7
Machine 2        2     12      6      5
Machine 3        7      8      3      9
Machine 4        2      4      6     10
```
Question 6. A company is taking bids on four construction jobs. Three people have placed bids on the jobs as shown in the following table ("*" indicates that the person did not bid on that job).
```
Job 1  Job 2  Job 3  Job 4

Person 1       50     46     42     40
Person 2       51     48     44      *
Person 3        *     47     45     45
```
Person 1 can do only one job but persons 2 and 3 can each do up to three jobs. Determine the minimum cost assignment of persons to jobs. [Winston 379-4]

Question 7. Woodco gets an order for 25 3-ft, 20 5-ft, and 15 9-ft pieces of lumber. It fills the order by cutting up stock 8-ft and 16-ft pieces of which it has a vast supply. How should the cutting be done to minimize waste.