Question

Problem 3-31 (Algorithmic)

Gulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, has inquired into the possibility of providing a portion of the reservoir capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only 0.5% of capacitors provided by Lyshenko had to be discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only 2% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston Components’ defective rate to be 9%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 73000 acceptable-quality capacitors to use in its electronic devices. To ensure that Boston Components will receive some of the contract, management specified that the volume of reservoir capacitors awarded to Boston Components must be at least 12% of the volume given to Able Controls. In addition, the total volume assigned to Boston Components, Able Controls, and Lyshenko Industries should not exceed 29000, 48000, and 47500 capacitors, respectively. Because of Gulf Coast’s long-term relationship with Lyshenko Industries, management also specified that at least 29500 reports should be ordered from Lyshenko. The cost per capacitor is $2.4 for Boston Components, $2.5 for Able Controls, and $2.8 for Lyshenko Industries.

1. Formulate and solve a linear program for determining how many reservoir capacitors should be ordered from each supplier to minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Enter "0" if your answer is zero. If the constant is "1" it must be entered in the box.
   
   Let B = number of capacitors ordered from Boston Components
   
   Let A = number of capacitors ordered from Able Controls
   
   Let L = number of capacitors ordered from Lyshenko Industries
   

   Min	B	+	A	+	L
   s.t.
   	B					≤		Boston
   			A			≤		Able
   					L	≤		Lyshenko
   	B ____	+	A____	+	L	=		# useful capacitors
   	B	+	A			≥		Boston - Able %
   					L	≥		Minimum Lyshenko
   B, A, L ≥ 0

   
   Round your answers to the nearest whole number.
   

   Optimal Solution:
   B	____
   A	____
   L	____

2. Suppose that the quality level for reservoir capacitors supplied by Boston Components is much better than estimated. What effect, if any, would this quality level have?
   
   If the quality of reservoir capacitors supplied by Boston Components is much better than expected the optimal solution may change. For example, if Boston Components reduced their defect rate from 9% to 2%, the new optimal solution would increase the number of reservoir capacitors given to Boston Components to .
   
3. Suppose that management is willing to reconsider their requirement that at least 30,000 capacitors must be ordered from Lyshenko Industries. What effect, if any, would this consideration have? If required, round your answer to the nearest cent.
   
   If management removes or reduces the requirement that Lyshenko Industries be ordered at least 30,000 reservoir capacitors the cost will decrease by $__________ per unit decreased.

Answer 1

(a)

Min	2.4 B	+	2.6 A	+	2.85 L
s.t.
	1 B					≤	29,000	Boston
			1 A			≤	52,000	Able
					1 L	≤	52,000	Lyshenko
	0.89 B	+	0.99 A	+	0.995 L	=	78000	# useful capacitors
	1 B	+	-0.12 A			≥	0	Boston - Able %
					1 L	≥		Minimum Lyshenko
B, A, L ≥ 0

Units from B	5268
Units from A	43900
Units from L	30000

(b)

The quality level for reservoir capacitors supplied by Boston Components is much better than estimated because the capacitors supplied by Boston would be closer to the constraints value of 29,000. If 1% defective rate is rectified, the new optimal solution would increase the increase the capacitors assigned to Boston up to 29,000.

(c)

The cost will decrease by $0.23 per unit decrease.