Brue Lee is the Vice President of Purchasing for the consumer electronics division of the Major Electric Corporation $($MEC$).$ The company recently introduced a new type of video camcorder that has taken the market by storm. Although Brue is pleased with the strong demand for this product in the market place, it has been a challenge to keep up with MEC$$s distributors$$ orders of this camcorder. His current challenge is how to meet requests from MEC$$s major distributors in Pittsburgh, Denver, Baltimore, and Houston who have placed orders of $10,000,20,000,30,000,$ and $25,000$ units, respectively, for delivery in $2$ months $($there is a $1-$month manufacturing and $1-$month shipping lead time for this product$).$

MEC has contracts with companies in Hong Kong, Korea, and Singapore who manufacture camcorders for the company under the MEC label. These contracts require MEC to order a specified minimum number of units each month at a guaranteed per unit cost. The contracts also specify the maximum number of units that may be ordered at this price. The following table summarizes these contracts:

Monthly Purchasing Contract Provisions

Supplier

Unit Cost

Minimum Required

Maximum Allowed

Hong Kong

$$375$

$20,000$

$30,000$

Korea

$$390$

$25,000$

$40,000$

Singapore

$$365$

$15,000$

$30,000$

MEC also has a standing contract with a shipping company to transport product from each of these suppliers to ports in San Francisco and San Diego. The cost of shipping from each supplier to each port is given in the following table along with the minimum required and maximum allowable number of shipping containers each month:

Monthly Shipping Contract Provisions

San Francisco Shipping Requirements

San Diego Shipping Requirements

Supplier

Cost per Container

Minimum Containers

Maximum Containers

Cost per Container

Minimum Containers

Maximum Containers

Hong Kong

$$2,000$

$5$

$20$

$$2,300$

$5$

$20$

Korea

$$1,800$

$10$

$30$

$$2,100$

$10$

$30$

Singapore

$$2,400$

$5$

$25$

$$2,200$

$5$

$15$

Under the terms of this contract, MEC guarantees it will send at least $20$ but no more than $65$ shipping containers to San Francisco each month, and at least $30$ but no more than $70$ shipping containers to San Diego each month.

Each shipping container can hold $1,000$ video cameras and will ultimately be trucked from the seaports on to the distributors. Again, MEC has a standing contract with a trucking company to provide trucking services each month. The cost of trucking a shipping container from each port to each distributor is summarized in the following table:

Unit Shipping Cost per Container

Pittsburgh

Denver

Baltimore

Houston

San Francisco

$$1,100$

$$850$

$$1,200$

$$1,000$

San Diego

$$1,200$

$$1,000$

$$1,100$

$$900$

As with the other contracts, to obtain the prices just given, MEC is required to use a certain minimum amount of trucking capacity on each route each month and may not exceed certain maximum shipping amounts without incurring cost penalties. These minimum and maximum shipping restrictions are summarized in the following table:

Minimum Required and Maximum Allowable Number of Shipping Containers per Month

Pittsburgh

Denver

Baltimore

Houston

Min

Max

Min

Max

Min

Max

Min

Max

San Francisco

$3$

$7$

$6$

$12$

$10$

$18$

$5$

$15$

San Diego

$4$

$6$

$5$

$14$

$5$

$20$

$10$

$20$

Brue is left with the task of sorting through all this information to determine the least cost purchasing and distribution plan to fill the distributor$$s requests. But because he and his wife have tickets to the symphony for this evening, he has asked you to take a look at this problem and give him your recommendations at $9$:$00$ tomorrow morning.

Create a network flow model for this problem. $($Hint: Consider inserting intermediate nodes in your network to assist in meeting the minimum monthly purchase restrictions for each supplier and the minimum monthly shipping requirements for each port.$)$

Implement a spreadsheet model for this problem and solve it$.$

What is the optimal solution?