Suppose that the sales forecasts have been revised downward to $280,400,$ and $350$ units per day

of products $1,2,$ and $3,$ respectively, and that each plant now has the capacity to produce all that

is required of any one product. Therefore, management has decided that each new product

should be assigned to only one plant and that no plant should be assigned more than one product

$($so that three plants are each to be assigned one product, and two plants are to be assigned none$).$

The objective is to make these assignments so as to minimize the total cost of producing these

amounts of the three products.

$($c$)$ Formulate this problem as an assignment problem by constructing the appropriate cost

table.

$($d$)$ Obtain an optimal solution.

$($e$)$ Reformulate this assignment problem as an equivalent transportation problem by

constructing the appropriate parameter table.

$($f$)$ Starting with Vogel$$s approximation method, interactively apply the transportation

simplex method to solve the problem as formulated in part $($c$).$

$($g$)$ From the context above, run both the transportation and assignment model R specifying

the packages employed and compare your optimal solutions with the calculated ones

from parts $($a$)$ to $($f$).$ You are expected to show your codes and results.