EXERCISES!!!! Please only answer question $2.$ A and B$!!!$

Skycell, a major European cell phone manufacturer, is making production plans for the coming year. Skycell has worked with its customers $($the service providers$)$ to come up with forecasts of monthly requirements $($in thousands of phones$)$ as shown in Table $8-10.$

Manufacturing is primarily an assembly operation, and capacity is governed by the number of people on the 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. Skycell currently has a no$-$layoff policy in place. Overtime is limited to a maximum of $20$ hours per month per employee. Assume that Skycell 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 ner 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 incress of allowed overtime per employee per month from $20$ hours to $40?$

TABLE $8-10$

Monthly Demand for Cell Phones, in Thousands

Month

January

February

March

April

May

June

July

August

September

October

NovemBer

December

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

d$.$ Consider part $($a$)$ for the case in which Skycell 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

$2.$ Reconsider the Skycell data in Exercise$1.$ Assume that the plant has $1,250$ employees and a no$-$layoff policy. Overtime is limited to $20$ hours per employee per month. A third party has offered to produce cell phones as needed at a cost of $$26$ per unit $($this includes component costs of $$20$ per unit$).$

a$.$ What is the average per unit cost of in$-$house production $($including inventory holding and overtime cost$)$ if the third party is not used?

b$.$ How should Skycell use the third party? How does your answer change if the third party offers a price of $$25$ per unit?

c$.$ Should Skycell use the third party if the per unit cost is $$28?$

d$.$ Why would Skycell use the third party even when the perunit cost of the third party is higher than the average perunit cost $($including inventory holding and overtime$)$ for in$-$house production?

$3.$ Reconsider the Skycell data in Exercise $1.$ Assume that the plant has $1,250$ employees and a no$-$layoff policy. Overtime is limited to at most $20$ hours per employee per month. Also assume no subcontracting option. Skycell has a team of $50$ people who are willing to work as seasonal employees. The cost of bringing them on is $800$ euros per employee, and the layoff cost is $1,200$ euros per employee.