$3.$ For the next four months, the following demands are expected: $500,650,1000$ and $700$ units. Unit production costs are $$50,$ $$80,$ $$40$ and $$70$ during the next four months respectively. For the first three months, a $$20$ per unit storage cost is assessed on each month$$s ending inventory. Any units on hand at the end of month $4$ can be sold for $$40$ per unit.

a$.$ Determine how to minimize the total cost of meeting demands for the next four months.

b$.$ Using SolverTable, what happens to the decision variables and total cost when the unit production cost of month $2$ varies from $$30$ to $$150$ in increments of $$10.$