Three fires have just broken out in New York. Fires 1 and 2 each require two fire engines, and fire 3 requires three fire engines. The “cost” of responding to each fire depends on the time at which...

Three fires have just broken out in New York. Fires 1 and 2 each require two fire engines, and fire 3 requires three fire engines. The “cost” of responding to each fire depends on the time at which the fire engines arrive. Let t_ij be the time (in minutes) when the jth engine arrives at fire i. Then the cost of responding to each fire is as follows:

Fire 1: 6t₁₁ + 4t₁₂

Fire 2: 7t₂₁ + 3t₂₂

Fire 3: 9t₃₁ + 8t₃₂ + 5t₃₃

Three fire companies can respond to the three fires.

Company 1 has three engines available, and companies 2 and 3 each have two engines available. The time (in minutes) it takes an engine to travel from each company to each fire is shown in Table.

a Formulate and solve a transportation problem that can be used to minimize the cost associated with as- signing the fire engines. (Hint: Seven demand points will be needed.)

b Would the formulation in part (a) still be valid if the cost of fire 1 were 4t₁₁ + 6t₁₂?