$9\mathrm{.}1-4$

The Versatech Corporation has decided to produce three new products. Five branch plants now have excess product capacity. The unit manufacturing cost of the first product would be $$49,$$$47,$$$50,$$$46,$ and $$47$ in Plants $1,2,3,4,$ and $5,$ respectively. The unit manufacturing cost of the second product would be $$63,$$$59,$$$64,$$$60,$ and $$61$ in Plants $1,2,3,4,$ and $5,$ respectively. The unit manufacturing cost of the third product would be $$56,$$$53,$ and $$58$ in Plants $1,2,$ and $3,$ respectively, whereas Plants $4$ and $5$ do not have the capability for producing this product. Sales forecasts indicate that $600,1,000,$ and $800$ units of products $1,2,$ and $3,$ respectively, should be produced per day. Plants $1,2,3,4,$ and $5$ have the capacity to produce $400,600,400,600,$ and $1,000$ units daily, respectively, regardless of the product or combination of products involved. Assume that any plant having the capability and capacity to produce them can produce any combination of the products in any quantity.

Management wishes to know how to allocate the new products to the plants to minimize total manufacturing cost.

$9\mathrm{.}1-4($a$)$

Formulate this problem as a transportation problem by constructing the appropriate parameter table.