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 1% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston Components' defective rate to be 11%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 78000 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, 52000, and 52000 capacitors, respectively. Because of Gulf Coast's long-term relationship with Lyshenko Industries, management also specified that at least 30000 reports should be ordered from Lyshenko. The cost per capacitor is $2.4 for Boston Components, $2.6 for Able Controls, and $2.85 for Lyshenko Industries a. 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 "O" 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 Industrie:s Min 2.4 B 2.6 A 2.85 L

Please answer the exact answer and I will definitely rate you like/ thumb up. Thank you!

Answer 1

(a)

Min 2.4B 2.6 A+ 2.85 L s.t 29,000 Boston | 52,000 |Able 1 A 1 L ls l 52,000 |Lyshenko 0.89 B |+10.99 |A |+| 0.995 L -1 78000 |# useful capacitors 1 8 0.12 A Boston-Able % | L | 30,000 | Minimum Lyshenko B, A, L20

(b)

B A L 3Units from Cost 2.4 2.62.85 SUMPRODUCT (SC$3 SES3,C4.EA) Boston -SUMPRODUCT($C$3:$E$3.C6 E6) <-29000 SUMPRODUCT SC$3SE$3,C7 ET)52000 -SUMPRODUCT($C$3:SE$3,C8E8) <-52000 SUMPRODUCT (SC$3:SE$3,C9 E9) 78000 SUMPRODUCT(SC$3 SE$3,C10E10)0 -SUMPRODUCT($C$3:$E$3.C11:E11) 7 Able 8 Lyshenko 9 #useful 10 Boston-Able % 1-0 12 11 Min L 0.89 0.99 0.995 )230000

Set Objective: O Max O Value Of: Min By Changing Variable Cells: C$3: $E$3 Subject to the Constraints: $F$10:$F$11 >= $H$10:$H$11 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Close Help Solve

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

(b)

May change. The new optimal solution will be B = 29,000 [Modify cell $C$9 from 0.89 to 0.98 and rerun the solver]

(c)

Variable Cells Final Value 5268.052516 43900.43764 Reduced Objective Allowable Allowable st Coefficient Increase Decrease Cell SC$3 Units from B $D$3 Units from A SE$3 Units from L Cos Name 2.4 2.113232831 0.062626263 1E+30 1E+30 0.230051058 2.6 0.069662921 2.85 30000 Constraints Final Shadow Constraint Allowable Allowable R.H. Side Increase Decrease 0 26292.12121 5836. 363636 Cell $F$10 Boston-Able % Name Value Price 9.09495E-13 0.056528082 30000 0.230051058 $F$11 Min L 30000 29000 52000 52000 78000 22000 8928.241206 1E+30 23731.94748 1E+30 8099. 5623бЗ 1E+30 8883.6 oston $F$7 $F$8 $F$9 Able Lyshenko # useful 43900.43764 22000 48150 30000 78000 2.633114515

The cost will decrease by $0.23 per unit decrease.