$9\mathrm{.}1-6.$ The Move$-$It Company has two plants producing forklift trucks that then are shipped to three distribution centers. The production costs are the same at the two plants, and the cost of shipping for each truck is shown for each combination of plant and distribution center: A total of $60$ forklift trucks are produced and shipped per week. Each plant can produce and ship any amount up to a maximum of $50$ trucks per week, so there is considerable flexibility on how to divide the total production between the two plants so as to reduce shipping costs. However, each distribution center must receive exactly $20$ trucks per week. Management$$s objective is to determine how many forklift trucks should be produced at each plant, and then what the overall shipping pattern should be to minimize total shipping cost. $($a$)$Formulate this problem as a transportation problem by constructing the appropriate parameter table.