Solve in excel and show all steps clearly and completely.

Q$4$: Sky cell, a major cell phone manufacturer, is making production plans for the coming year. Sky cell has worked with its customers $($the service providers$)$ to come up with forecasts of monthly requirements $($in thousands of phones$)$ as shown in Table Manufacturing is primarily an assembly operation, and capacity is governed by the number of people on the

$\backslash$table$[[$Months$,$Demand$],[$January$,900],[$February$,1000],[$March$,900],[$April$,1100],[$May$,1100],[$June$,1000],[$July$,1000],[$August$,1100],[$September$,900],[$October$,1200],[$November$,1200],[$December$,1000]]$

production line. The plant operates for $20$ days a month, eight hours each day. One person can assemble a phone every $10$ minutes. Workers are paid $20$ euros per hour and a $50$ percent premium for overtime. The plant currently employs $1,250$ workers. Component costs for each cell phone total $20$ euros. Given the rapid decline in component and finished product prices, carrying inventory from one month to the next incurs a cost of $3$ euros per phone per month. Sky cell currently has a no$-$layoff policy in place. Overtime is limited to a maximum of $20$ hours per month per employee. Assume that Sky cell has a starting inventory of $50,000$ units and wants to end the year with the same level of inventory.

a$)$ Assuming no backlogs, no subcontracting, and no new hires, what is the optimum production schedule? What is the annual cost of this schedule?

b$)$ Is there any value for management to negotiate an increase of allowed overtime per employee per month from $20$ hours to $40?$

c$)$ Reconsider parts $($a$)$ and $($b$)$ if Sky cell starts with only $1,200$ employees. Reconsider parts $($a$)$ and $($b$)$ if Sky cell starts with $1,300$ employees. What happens to the value of additional overtime as the workforce size decreases?$\text{'}$

d$)$ Consider part $($a$)$ for the case in which Sky cell aims for a level production schedule such that the quantity produced each month does not exceed the average demand over the next $12$ months $(1,241,667)$ by $50,000$ units. Thus, monthly production, including overtime, should be no more than $1,291,667.$ What would be the cost of this level production schedule? What is the value of overtime flexibility?