Linear Programming Problem

XYZ Lawn Trimmer Company produces two types of lawn trimmers – a gas model and an electric model. The company has two manufacturing facilities: San Diego and Atlanta. Both plants have the capability to produce both of the models but the manufacturing and transportation costs are different.

 

San Diego Atlanta Demand Gas $125 $100 225 Electric $115 $95 275

Capacity 400 units 200 units Storage Space 10,000 sq ft 5,000 sq. ft Leased WH Cost $5 per sq. ft $4 per sq ft. Leased WH Capacity 15,000 sq ft $18,000 sq ft.

 

The company has just received a contract from a large retailer for the production of 225 gas models and 275 electric models. The San Diego plant can produce up to 400 units and the Atlanta plant can produce up to 200 units. Because the manufacturing facilities have limited storage space, there is concern that space will have to be rented to store the finished products. The San Diego plant has 10,000 sq ft available on site, and the Atlanta plant has 5,000 sq ft on site. After this space is filled, off-site space will have to be rented. All of the models require about the same square footage (about 30 square feet), but the price for rental space in each of the locations is different. The rental price in San Diego is $5 per square foot and the price in Mexico is $4 per square foot. There are 15,000 sq ft available in San Diego and 18,000 sq ft available in Atlanta.

Formulate a linear programming model to minimize total cost. Be sure to define your decision variables. Determine how many of each type will be manufactured in San Diego and Atlanta, and also determine if any additional storage space is needed.