Question

a) Determine a minimum inventory production plan (i.e., one that allows arbitrary hiring and firing). b) Determine the production plan that meets demand but does not hire or fire workers during the six-month period. c) Let’s say subcontracting is allowed. Let’s say we implement the constant workforce with subcontracting plan, what would the cost of subcontracting need to be to beat the cheaper of the two options above? d) Using this subcontracting cost of $50, formulate a LP and solve to optimality for the constraints of this problem

Answer 1

To determine a minimum inventory production plan, the firm should consider arbitrary hiring and firing. They can optimize their production process to meet demand without hiring or firing workers. If subcontracting is allowed, the cost of subcontracting needs to be lower than other options to be cost-effective.

Step-by-step explanation:

a) To determine a minimum inventory production plan, the firm should consider arbitrary hiring and firing. This means that they can adjust their labor force as needed to meet demand. They should produce enough products to meet the demand while minimizing the cost of labor and inventory.

b) To meet demand without hiring or firing workers, the firm should carefully plan their production process. This could involve optimizing production methods, adjusting working hours, or outsourcing certain tasks.

c) If subcontracting is allowed, the firm can implement a constant workforce plan with subcontracting. The cost of subcontracting needs to be lower than the cost of hiring and firing workers in order for it to be a more cost-effective option.

d) With a subcontracting cost of $50, the firm can formulate a linear programming (LP) problem to optimize the constraints and find an optimal solution. This LP problem will consider the cost of labor, subcontracting, and other relevant factors to determine the best production plan.

Answer 2

Hello your question is incomplete attached below is the complete question

answer:

A) 32 units ( number of units per month per worker )

B) number of workers required = 975 / 32 ≈ 31

c) mean of the two values = 138 + 41 ) / 2 = $89.50

Step-by-step explanation:

A) Determine a minimum inventory production plan ( i.e. one that allows arbitrary hiring and firing )

The number of units per month per worker = 32 units

To have a minimum/least inventory; production plan = demand by hiring or firing

of employees

attached below is the table

B) determine the production plan that meets demand but does not hire or fire workers during the six-month period

To determine this production plan we have to find the per month production = (Total demand - beginning inventory ) / 6

= ( 6350 - 500 ) / 6 = 975 units produced

number of workers required = 975 / 32 ≈ 31

C) Calculate The cost of subcontracting needed to beat the cheaper of the two options above

regular cost = 8 * 5 = $40

we will keep 30 workers in order to determine how much subcontracting is needed and the maximum and minimum value of each unit is kept hence the overall cost < $253900.

if subcontracting cost = $138 then total cost = $253820

If subcontracting cost = $41 then total cost = $245090.

Therefore mean of the two values = 138 + 41 ) / 2 = $89.50

D) subcontracting cost of $50 formulating a LP and solve to optimality for the constraints of this problem

Z <= (Y+1)*7680 , X + 32Y >= 5850