TimsTabletCo $($TTC$)$ produces tablet computers, and it must determine the number of units to be produced during each of the

next four months. The following table gives the monthly demand and the monthly cost of producing each unit:

At the start, before Month $1,$ TTC has an inventory of $2000$ units. Each month, up to $4000$ units can be produced. TTC can use

the units produced in a particular month in two ways: either use some units to satisfy the demand in the same month, or store

some units in inventory for future use. The cost of storing units in inventory is $$100$ per unit per month.

$($a$)$ Formulate an LP problem $(P)$ to minimize the total cost of meeting the demands of the next four months.

$($b$)$ Write the dual LP $($D$)$ of $($P$).$

If youre answering one, please answer part b$.$