Two plants with different capacities of boat production per month. Plant 1 can produce 60 boats per month, and Plant 2 capacity is 80 boats per month. The cost of producing each boat is $9000, $10,000 in Plants 1 and 2, respectively. The produced boats are transported from these two plants to two warehouses located in New York and Washington. The cost of transporting each boat from each plant to each warehouse has been provided in the table below:

From NY Washington

Plant 1 $60 $80

Plant 2 $50 $45

The demand of each warehouse is different. The warehouse in New York has a demand for 90 boats per month, and the demand of Washington warehouse is 70 boats per month. There is a penalty for unmet demand. The penalty of unmet demand is respectively $400 and $500 for New York to Washington warehouses. Formulate this problem using linear programing to find the optimal configuration. There is no need to solve your formulated problem to determine the optimal solution.