The demand forecast made by the marketing department of gas stoves for different variants of a popular model of gas stove given below

Month Demand$($Units$)$

Jan $1600$

Feb $1400$

Mar $1800$

Apr $2000$

May $1500$

a$)$ Develop an aggregate production plan for Jan to MAY. The plan should first meet the demand using the available man power and then subcontracting.

b$)$ Draw a neat and well labelled graph of the aggregate plan.

c$)$ What is the total cost of this aggregate plan? $($Show$/$ Explain every calculation$)$

$($The company has $200$ numbers of stoves in the inventory at the beginning of Jan and it wants to keep the same level of inventory, inventory holding cost is Rs$\mathrm{.}150$ per unit$/$month$,$ the number of workers in the company are $12,$ output$/$workers$/$month$=90$ units, average salary of the worker$=$Rs$\mathrm{.}30000/$month$.$ Subcontracting cost is Rs$\mathrm{.}400/$unit$)$