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A company produces 2 end products: A and B. Product A is assembled out of 2 components: component A1 and common component AB. Product B is also assembled out of 2 components: common component AB and component B1.

In order to produce these end products, the company can make use of 8 types of machines (M1, M2, M3, M4, M5, M6, M7 and M8). For each type there is 1 machine available. The machines operate 2400 minutes per week (= 5 days = 40 hours). The machines have no setups.

Each machine produces the products one by one.

The components undergo the following sequence of operations:

Component A1: M6 (24,5 minutes per unit), M2 (5 minutes per unit), M1 (20 minutes per unit)
Component AB: M7 (15 minutes per unit), M4 (15 minutes per unit)
Component B1: M8 (5 minutes per unit), M3 (20,5 minutes per unit), M1 (12 minutes per unit).

The assembly takes place on machine M5 and this for both end products. The processing time for end product A on the M5 is 20 minutes per unit while for end product B the processing time amounts 14 minutes per unit.

1. Draw the bill of manufacture:


Product A
Part #	Part name	The machines needed	Description	Timerequired (In min)	Quantity	Units	Unit cost	Total Cost	Selling Price
1	A1	M1, M2 and M6					10	20	100
	M1		Machines used in A1	20	1	1
	M2		Machines used in A1	5	1	1
	M6		Machines used in A1	24.5	1	1
2	AB	M4, M7					10
	M4		Machines used in AB	15	1	1
	M7		Machines used in AB	15	1	1
3	Assembling	M5	Assembling of components	20	1	1


Product B
Part #	Part name	The machines needed	Description	Time	Quantity	Units	Unit cost	Total Cost	Selling Price
1	AB	M4, M7					10	20	90
	M4		Machines used in AB	15	1	1
	M7		Machines used in AB	15	1	1

2	B1	M1, M3 and M8					10
	M1		Machines used in B1	12	1	1
	M3		Machines used in B1	20.5	1	1
	M8		Machines used in B1	5	1	1
3	Assembling	M5	Assembling of components AB and B1	14	1	1

2. Assume that both machine M1 and M6 break down each 7 hours on average. The breakdown lasts for 1 hour. Assume also that the maximum demand for end product A equals 60 units per week and 90 units per week for end product B. Determine the bottleneck. Please provide all necessary calculations and explanаtions!

Minutes	Hours	Break Through Hour	Hour available	Shifts
2400	40	5	35	5

Break Through Hour	Break Through minutes	Net Available mints
5	300	2100

	Machines	Time		Units
				A1	Total Available	Remaining
Limited	m1	20	1200	60	2100	900
	m2	5	300	60	2400	2100
Limited	m6	24.5	1470	60	2100	630

				Units
AB
	m7	15	2400	160	2400	0
150	m4	15	2400	160	2400	0

B1
	m8	5	2400	480		2400
	m3	20.5	2400	117		2400
	m1	12	900	75		900

		180	15	90	Need to complete the demand


A1+AB	Units of Prod A	60	(no bottle neck)
AB+B1	Units of Prod b	90

Machines M1 and M6 are used in the production of product A. Components that has been made with the help of machine M1 and M6 are A1. In the production of the A1, the M1 takes 20 minutes to produce one unit. Maximum demand for product A equals to 60 units it means the total minutes required to produce 60 units at M1 is equal to 122 minutes. Likewise, the total units that will be made on M2 and M6 are 2400 and 2100 respectively. On the component A1, there is no bottleneck. Machines M1 and M6 are manufactured according to the demand. However, M2 is producing more than the demand that is not even required because it will end up in increasing inventories. Here M2 can be treated as a bottleneck.

In the manufacturing of AB, machines that are used are the M4 and M7, and there is no restriction in terms of time on both the machines. In the manufacturing of component B1, machines used in it are M1, M3 and M8. The calculations have shown that the units produce in 7 hours is 180 units. However, the demand of the company has been just 90 units. Thus, extra production should be stopped because it will become a bottleneck in the near future in terms of excess inventories. The calculations have shown that units of product A produced in a week is 6 and there is no bottleneck in it...............................

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