Math Forum / Mathematics / Algebra Help / September 2008

The Sentry lock Corporation manufactures a popular commerical security lock
at plants in Macon, Louisville, Detroit, and Phoenix. the per unit cost of
production at each plant is $35.50, $37.50, $39.00, $36.25 respectively, and
the annual production capacity at each plant is 18000, 15000, 25000, 20000,
respectively. Sentry's locks are sold to retailers through wholesale
distributors in seven cities across the US. The unit cost of shipping from
each plant to each distributor is summarized in the following table along
with the forecastd demand from each distributor for the coming year..

Plants    Tacoma   San Diego   Dallas    Denver   St.Louis   Tampa
Baltimore
Macon      2.50      2.75               1.75     2.00       2.10      1.80
1.65
Louisville  1.85      1.90                1.50    1.60       1.00      1.90
1.85
Detroit      2.30      2.25               1.85    1.25       1.50      2.25
2.00
Phoenix   1.90       .90                1.60     1.75       2.00     2.50
2.65

Demand 8500      14500            13500   12600    18000   15000
9000

Sentry wants to determine the least expensive way of manufacturing and
shipping locks from their plants to the distributors, Because the total
demand from distributors be able to satisfy all the demand for its product,
but wants to make sure each distributor will have the opportunity to fill at
least 80% of the orders they receive.  

a. What is the optimal solution?