Problem 3-31 (Algorithmic)
Gulf Coast Electronics is ready to award contracts to suppliersfor providing reservoir capacitors for use in its electronicdevices. For the past several years, Gulf Coast Electronics hasrelied on two suppliers for its reservoir capacitors: Able Controlsand Lyshenko Industries. A new firm, Boston Components, hasinquired into the possibility of providing a portion of thereservoir capacitors needed by Gulf Coast. The quality of productsprovided by Lyshenko Industries has been extremely high; in fact,only 0.5% of capacitors provided by Lyshenko had to be discardedbecause of quality problems. Able Controls has also had a highquality level historically, producing an average of only 2%unacceptable capacitors. Because Gulf Coast Electronics has had noexperience with Boston Components, it estimated Boston Components’defective rate to be 9%. Gulf Coast would like to determine howmany reservoir capacitors should be ordered from each firm toobtain 73000 acceptable-quality capacitors to use in its electronicdevices. To ensure that Boston Components will receive some of thecontract, management specified that the volume of reservoircapacitors awarded to Boston Components must be at least 12% of thevolume given to Able Controls. In addition, the total volumeassigned to Boston Components, Able Controls, and LyshenkoIndustries should not exceed 29000, 48000, and 47500 capacitors,respectively. Because of Gulf Coast’s long-term relationship withLyshenko Industries, management also specified that at least 29500reports should be ordered from Lyshenko. The cost per capacitor is$2.4 for Boston Components, $2.5 for Able Controls, and $2.8 forLyshenko Industries.
- Formulate and solve a linear program for determining how manyreservoir capacitors should be ordered from each supplier tominimize the total cost of obtaining 75,000 acceptable-qualityreservoir capacitors. For subtractive or negative numbers use aminus sign even if there is a + sign before the blank. Enter \"0\" ifyour answer is zero. If the constant is \"1\" it must be entered inthe box.
Let B = number of capacitors ordered from BostonComponents
Let A = number of capacitors ordered from AbleControls
Let L = number of capacitors ordered from LyshenkoIndustries
| 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 | ____ |
- Suppose that the quality level for reservoir capacitorssupplied by Boston Components is much better than estimated. Whateffect, if any, would this quality level have?
If the quality of reservoir capacitors supplied by BostonComponents is much better than expected the optimal solution maychange. For example, if Boston Components reduced their defect ratefrom 9% to 2%, the new optimal solution would increase the numberof reservoir capacitors given to Boston Components to .
- Suppose that management is willing to reconsider theirrequirement that at least 30,000 capacitors must be ordered fromLyshenko Industries. What effect, if any, would this considerationhave? If required, round your answer to the nearest cent.
If management removes or reduces the requirement that LyshenkoIndustries be ordered at least 30,000 reservoir capacitors the costwill decrease by $__________ per unit decreased.
