A manufacturer of batteries for mobile phones, signed a contract with a large electronics manufacturer to produce three models of lithium -ion battery packs for a new line of phones. The contract calls for the following:

Battery pack Production Quantity

Type 1 Battery: 200,000 Units

Type 2 Battery: 100,000 Units

Type 3 Battery: 150,000 Units

They can manufacture the battery packs at manufacturing plants located in the Philippines and Mexico. The unit cost of the battery packs differs at the two plants because of differences in production equipment and wage rates. The unit costs for each battery pack at each manufacturing plant are as follows:

Product Philippines Mexico

Type 1:

Mexico, $1.08, Philippines, $1.13

Type 2:

Mexico, $1.16 Philippines $1.16

Type 3:

Mexico $1.25, Philippines $1.52

The combines production capacities for Type 1 and Type 2 are 175,000 units at the Philippines plant, and 160,000 units at the Mexico plant. The type 3 production capacities are 75,000 units at the Philippines plant and 100,000 units at the Mexico plant. Determine how many units of each type to produce at each plant to minimize the total production cost to satsify the customer demand for each type. Take into consideration the limited capacities of each manufacturing product.

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