$(6\mathrm{.}16.*)$ The Medequip Company produces precision medical diagnostic equipment at two factories. Three medical centers have placed orders for this month's production output. The following table shows what the cost would be for shipping each unit from each factory to each of these customers. Also shown are the number of units that will be prodtued at each factory and the number of units ordered by etach customer.

A decision now needs to to made about the shipping plan for how many units to ship from each factory to cach customer.

a$.$ Which category of linear programming problem does this problem fit? Why?

b$.$ Formulate and solve a linear programming model for this problem on a precadsheet Summarize this formulation in algebratc form.