Individual Assignment

Quantitative analysis for Management Decision

1. Explain in detail the following concepts

Quantitative analysis

Model

Linear programming

2. Back Savers is a company that produces backpacks primarily for students. They are considering offering some combination of two different modelsthe Collegiate and the Mini. Both are made out of the same rip-resistant nylon fabric. Back Savers has a long-term contract with a supplier of the nylon and receives a 5,000-squarefoot shipment of the material each week. Each Collegiate requires 3 square feet while each Mini requires 2 square feet. The sales forecasts indicate that at most 1,000 Collegiates and 1,200 Minis can be sold per week. Each Collegiate requires 45 minutes of labor to produce and generates a unit profit of $32. Each Mini requires 40 minutes of labor and generates a unit profit of $24. Back Savers has 35 laborers that each provides 40 hours of labor per week. Management wishes to know what quantity of each type of backpack to produce per week.

a.Formulate and solve a linear programming model for this problem.

b.Use the graphical method to solve this model.

c.Solve for Slack

3. A company imports goods at two ports: Lisbon and Le Havre. Shipments of one of its products are made to customers in Paris, Berlin, London and Milan. For the next planning period, the supplies at each port, customer demands and the shipping costs($) per case from each port to each customer are as follows:

Port	Customer	Port Supply
Paris	Berlin	London	Milan
Lisbon	2	6	6	2	5 000
Le Havre	1	2	5	7	3 000
Demand	1 400	3 200	2 000	1 400

a. Develop a network model of the distribution system for this problem.

b. Test the necessary assumptions for to use transportation model.

c. Develop

d. Solve the problem to determine the minimum cost-shipping schedule.

4. Westside Auto purchases a component used in the manufacture of automobile generators directly from the supplier. Westsides generator production operation, which is operated at a constant rate, will require 1000 components per month throughout the year (12,000 units annually). Assume that the ordering costs are $25 per order, the unit cost is $2.50 per component, and annual holding costs are 20% of the value of the inventory. Westside has 250 working days per year and a lead time of 5 days. Answer the following inventory policy questions:

a. What is the EOQ for this component?

b. What is the reorder point?

c. What is the cycle time?

d. What are the total annual holding and ordering costs associated with your recommended EOQ?

5. The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in dollars) from each plant to each warehouse are as follows:

Plant	Warehouse	Capacity
1	2
1	4	7	450
2	8	5	600
3	5	6	380

Customer demand and shipping costs per unit (in dollars) from each warehouse to each customer are

Warehouse	Customer
1	2	3	4
1	6	4	8	4
2	3	6	7	7
Demand	300	300	300	400

a. Develop a network representation of this problem.

b. Formulate a linear programming model of the problem.

Solve the linear program to determine the optimal ship