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, 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 the 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 1% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston’s defective rate to be 10%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 75,000 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 10% of the volume given to Able Controls. In addition, the total volume assigned to Boston Components, Able Controls, and Lyshenko Industries should not exceed 30,000, 50,000, and 50,000 capacitors, respectively. Because of the long-term relationship with Lyshenko Industries, management also specified that at least 30,000 capacitors should be ordered from Lyshenko. The cost per capacitor is $2.45 for Boston Components, $2.50 for Able Controls, and $2.75 for Lyshenko Industries.

a. Formulate and solve a linear program for determining how many reservoir capacitors should be from each supplier to minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors. If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.

Let B = number of copies done by Boston Components

Let A = number of copies done by Able Controls

Let L = number of copies done by Lyshenko Industries

Min

____B

+

____A

+

____L

s.t.

____B

≤
_____
Boston

______A

≤
_____
Able

L

≤
_____
Lyshenko

______B

+

_____A

+

____L

=
_____
# useful reports

_____B

+

______A

≥
_____
Boston - Able %

______L

≥
______
Minimum Lyshenko

B, A, L ≥ 0

Optimal Solution:

B _____________

A _____________

L ______________

b.Suppose that the quality level for Boston Components is much better than estimated. What effect, if any, would this quality level have?
___________________________________________________________________

c. Suppose that management is willing to reconsider its requirement that at least 30,000 capacitors must be ordered from Lyshenko Industries. What effect, if any, would this consideration have?
_________________________________________________________________________

Question

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, 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 the 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 1% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston’s defective rate to be 10%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 75,000 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 10% of the volume given to Able Controls. In addition, the total volume assigned to Boston Components, Able Controls, and Lyshenko Industries should not exceed 30,000, 50,000, and 50,000 capacitors, respectively. Because of the long-term relationship with Lyshenko Industries, management also specified that at least 30,000 capacitors should be ordered from Lyshenko. The cost per capacitor is $2.45 for Boston Components, $2.50 for Able Controls, and $2.75 for Lyshenko Industries.

a. Formulate and solve a linear program for determining how many reservoir capacitors should be from each supplier to minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors. If required, round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.

	Let B = number of copies done by Boston Components
	Let A = number of copies done by Able Controls
	Let L = number of copies done by Lyshenko Industries

Min	____B	+	____A	+	____L
s.t.
	____B					≤	_____	Boston
			______A			≤	_____	Able
					L	≤	_____	Lyshenko
	______B	+	_____A	+	____L	=	_____	# useful reports
	_____B	+	______A			≥	_____	Boston - Able %
					______L	≥	______	Minimum Lyshenko
B, A, L ≥ 0

Optimal Solution:
B _____________
A _____________
L ______________

b.Suppose that the quality level for Boston Components is much better than estimated. What effect, if any, would this quality level have?
___________________________________________________________________

c. Suppose that management is willing to reconsider its requirement that at least 30,000 capacitors must be ordered from Lyshenko Industries. What effect, if any, would this consideration have?
_________________________________________________________________________

Accepted Answer

Solution:
(a): Let the no. of capacitors that has to be ordered from Able be “x”, from Lyshenko be…