Reference no: EM133063407

Question 1. [Transportation] J'Vita Ultra-Trendy Supply (JUTS) is a wholesale distributor of supplies for beauty and barbershops. JUTS can maintain wholesale centres for Clearall products, its most profitable line, only in two locations: Winnipeg and Montreal. JUTS ships Clearall products to retail outlets in Edmonton, Toronto, and Halifax.

This month, JUTS Montreal centre has 1800 cases of Clearall products available for shipment, while its Winnipeg centre can ship 1300 cases. The Edmonton outlet places a monthly order of 1000 cases, Toronto an order of 1500 cases, while Halifax an order of 600 cases. Carol Smith, the manager of JUTS, has worked out a table of costs per case for shipping as shown in the table below, and she is interested in reducing the shipping cost as much as possible while meeting customer demand.

asd	Edmonton	Toronto	Halifax	Available
Winnipeg	$5	$5	$7	1300
Montreal	$3	$2	$4	1800
Need	1000	1500	600

Formulate the problem as an LP problem to satisfy demand in Edmonton, Toronto, and Halifax while minimizing transportation costs. Do not solve!

Question 2. [Scheduling, 20 points] Catatonic manufactures and sells accessories for cats. They operate a call center for customer questions and complaints from 10am EST to 8pm EST seven days per week. Customer service staff work 4 days and then get 3 days off in a continuous rotation. That is, they work the same 4 days every week. Call volumes are reasonably stable through the year but do fluctuate by day of the week with most calls coming on weekends. The estimated staffing requirements for each day of the week are as follows:

	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
Min # staff	15	12	10	14	18	24	26

The base pay for staff is $14/hour or $140 per 10-hour day. However, there has been excessive turnover among the many staff that work Saturday or Sunday and Catatonic has agreed to pay staff $16/hour on Saturday and Sunday.

Formulate an LP model that will assist Catatonic to staff the call center at minimum weekly cost. Do not solve!

Question 3. [Investment, 24 points] International City Trust (ICT) has $5 million available for investment and wishes to maximize the interest earned on its investment over the next year. The specifics of the investment possibilities are shown in the Table below.

Investment	Interest Earned (Return on Investment)
Trade Credits	7%
Corporate bonds	10%
Gold stocks	19%
Platinum stocks	12%
Mortgage securities	8%
Construction loans	14%

To encourage diversified investment portfolio, the board of directors has placed several limits on the amount that can be committed to any one type of investment:

(1) No more than 25% of the total amount invested may be in any single type of investment,
(2) At least 30% of the funds invested must be in precious metals,
(3) At most 45% must be invested in trade credits and corporate bond.
Formulate the problem as an LP model that maximizes the interest earned on its investments over the next year such that the conditions specified in the table above are met. Do not solve!

Question 4. [Production Inventory, 36 points] Catatonic wishes to develop a model to assist in scheduling production of its soft-sided cat carriers. These items are made of fabric and have zippered openings to put the cat in the carrier and screened sides to allow the cat to see out. The major labor component is stitching the various pieces of fabric together. Demand for the two most popular models are as follows:

	January	February	March	April
Small	2,000	3,000	4,000	5,000
Medium	1,000	1,000	2,000	2,000

It takes 6 minutes to stitch a small carrier and 7 minutes to stitch a medium carrier. Catatonic has 500 hours of stitching time available each month. The cost to make one small carrier is $6.00, but this will increase to $6.20 in April. The cost to make a medium carrier is $7.50, increasing to $7.80 in April. Carriers made one month but not shipped until later, cost Catatonic $0.30 per unit per month in storage and handling costs. This cost is the same for both small and medium carriers. Catatonic currently has 200 small and 400 medium carriers in inventory and would like to have 500 of each size in inventory at the end of April.

Formulate an LP model that will assist Catatonic in deciding how many of each product to make each month such that total costs are minimized. Do not Solve!

Question 5. [Binary Integer Programming, 20 points] Catatonic is considering investments for the coming year. They are considering opportunities for new products, product redesigns, and process improvements. Proposals have been solicited from various departments within the firm with estimates of additional profit or cost savings, after expenses, that can be expected in the next three years if the project is selected. Managers have been asked what new investment will be required to launch the projects and their assessment of the likelihood that the profit/savings goal will be realized. The projects are summarized below:

Project	Profit/Saving	Cost	Project type	Likelihood of success
Cat backpack	$150,000	$150,000	New	High
Expandable airline carrier	$90,000	$165,000	Redesign	High
Catnip clothing	$60,000	$100,000	New	Moderate
Cat tree and scratching post	$80,000	$60,000	Redesign	Very high
Cat walking harness	$30,000	$70,000	New	Moderate
Automated packaging line	$40,000	$240,000	Process change	High
New supply chain IT system	$160,000	$400,000	Process change	Moderate

- They have a budget of $1,000,000 for New projects.
- They try to experiment with at least one new product per year and redesign at least one existing product each year.
- Process change is important with the board of directors and they should make some investment in this area.
- Although the new packaging line is attractive, it will require the new supply chain IT system to be successful (if they select packaging line, they must select IT).
- Management is risk averse and does not like to take on more than one "moderate" risk project (project proponents are notorious with respect to underestimating cost and risk).
- The cat backpack and airline carrier serve the same type of buyer. They will introduce at most one of the two.

Formulate an IP model that will assist Catatonic in selecting which project to pursue such that profits/savings are maximized while addressing all other restrictions. Do not solve!