quantitative week 5

Homework 3

1. The Childfair Company has three plants producing child push chairs that are to be

shipped to four distribution centers. Plants 1,2 and 3 produce 12, 17, and 11 shipments

per month, respectively. Each distribution center needs to receive 10 shipments per

month. The distance from each plant to the respective distribution centers is given below:

(Read pp. 425-431 & pp.480-484) (30 points)

Distance to Distribution Center (Mile)

1 2 3 4

Plant

1 800 1,300 750 700

2 1100 1,400 900 1,100

3 600 1,300 800 900

The freight cost for each shipment is $85 plus 55 cents mile. How much should be

shipped from each plant to each of the distribution centers to minimize the total shipping

cost? Formulate this problem as a transportation problem on a spreadsheet and then use

the Excel Solver to obtain an optimal solution. Also, interpret the results using at least

150 words by addressing the following issues. Also, please make sure you provide

answer report you obtained from Excel Solver.

a. What is the optimal mix of shipments from each plant to each of the distribution

center?

b. What is the minimum cost that could be achieved?

2. The following table shows the unit shipping cost between cities, the supply at each source

city and demand at each destination city. (Read pp. 425-431 & pp.480-484) (30 points)

Destination

Source Terre Haute Indianapolis Ft. Wayne South Bend Supply

St. Louis 8 6 12 9 100

Evansville 5 5 10 8 100

Bloomington 3 2 9 10 100

Demand 150 60 45 45

a. Given this table, set up a linear programming model as shown in page 428 for this

transportation problem

b. Provide the optimal solution using Solver in Excel. You must provide the optimal unit

of products shipped from each source city to each destination city, and total minimum

cost

c. Discuss any biblical principles that could be relevant to business issues (This is an open-

ended question and therefore there is no definite answer.)