A factory manufacturing two products(Product A and Product B) using two machines(Machine 1 and Machine 2) follows an optimal production plan that is consistent with maximum available hours of each machine(130 hours/month for Machine 1 and 120 hours/month for Machine 2), total available raw material(100 units of material) and available labor hours(200 hrs./month). Each hour of labor costs $10, each hour of work in Machine 1 costs $1, Machine 2 costs $1.50. Each unit of raw material costs $5. Product A is sold for $70 and Product B is sold for $55. When the cost of machines, materials and labor is deduced, their unit profits are $4 for Product A and $3.75 for Product B(notice, they would change depending on the cost items) Their usage of material and hours is shown in the table. Due demand limitations, they cannot produce more than 35 units of A, and they must produce at least 10 units of B.

	Product A	Product B	Variable Cost per hour
Machine 1	3 hrs.	1 hrs.	$1
Machine 2	2hrs	3.5 hrs.	$1.50
Labor	5 hrs.	4 hrs.	$10
Raw Material	2 units	1 units	$5
Price	$70	$55
Profit	$4	$3.75

The operations manager and her team solved for the optimal production plan and generated the following sensitivity analysis table.

					Final	Reduced	Objective	Allowable	Allowable
Cell		Name			Value	Cost	Coefficient	Increase	Decrease
$F$7		Product A			23.16	0.00	4.00	0.69	1.86
$G$7		Product B			21.05	0.00	3.75	3.25	0.55
					Final	Shadow	Constraint	Allowable	Allowable
Cell		Name			Value	Price	R.H. Side	Increase	Decrease
$H$17		Min Product B			21.05	0.00	10.00	11.05	1E+30
$H$18		Max Product A			23.16	0.00	35.00	1E+30	11.84
$H$19		Total Hours in Machine 1			90.53	0.00	130.00	1E+30	39.47
$H$20		Total Hours in Machine 2			120.00	0.29	120.00	55.00	21.00
$H$21		Total Labor Hours			200.00	0.68	200.00	32.14	62.86
$H$22		Total Available Material			67.37	0.00	100.00	1E+30	32.63

They consider several options to increase profitability. Please write your suggested course of action and the expected change in profit for the following problems.

There is a possible modification to Machine 

1). If this modification is done, the hourly cost of operating Machine 1 would decrease to $0.80. This modification costs $15. Can we decide on whether to make this modification using the Sensitivity Table? Write the value that you calculate to check if we can use the Sensitivity Table to solve.

2). Consider the sensitivity table in the previous question.

They can negotiate with the worker to work overtime. The worker currently asks for $15/hr. What would be the maximum wage the firm can offer for overtime within those hours? (Current wage is $10). Write your answer with two decimals.

3). Continue from the sensitivity table above.

You have offered the wage in the previous question, the worker said with this wage he would like to work like at least 50 hours of over-time. How many hours of overtime can you offer with that wage?

4). Using the same sensitivity table as previous questions, please answer the following:

There is a new product that they can start to produce. This product takes 4 hours at each machine, and requires a total of 8 hours of labor time. This product uses 15 units of raw material. What would be the minimum price that would make this product attractive? (Assume the product is attractive at break-even)

Answer rating: 100% (QA)

1 To determine if it is profitable to make the modification to Machine 1 we can use the sensitivity ... View the full answer