Free Essay

Quitmeyer Electronics

In: Business and Management

Submitted By robbieROB
Words 1331
Pages 6
robbie rob ds2 / bgen335– t@ beckley cu2014

Problem # 8-12. | page 324

Quitmeyer Electronics Incorporated manufacturers the following six microcomputer peripheral devices: internal modems, external modems, graphics circuit boards, CD drives, hard disk drives, and memory expansion boards. Each of these technical products requires time, in minutes, on three types of electronic testing equipment, as shown in the table below. minutes to manufacture Test Device 1 Test Device 2 Test Device 3 Internal Modem 7minutes .117 hours 2 minutes .033 hours 5 minutes .083 hours External Modem 3m .050 h 5m .083 h 1m .017 h Circuit Board 12 m .200 h 3m .050 h 3m .033 h CD Drives 6m .100 h 2m .033 h 2m .033 h Hard Drives 18 m .300 h 15 m .250 h 9m .150 h Memory Boards 17 m .283 h 17 m .283 h 2m .033 h

The first two test devices are available 120 hours per week. The third (device 3) requires more preventive maintenance and may be used only 100 hours each week. The market for all six computer components is vast, and Quitmeyer Electronics believes that it can sell as many units of each product as it can manufacture. The table that follows summarizes the revenues and material costs for each product: DEVICE Internal Modem External Modem Circuit Board CD Drives Hard Drives Memory Boards REVENUE PER UNIT SOLD ($) 200 120 180 130 430 260 MATERIAL COST PER UNIT ($) 35 25 40 45 170 60

In addition, variable labor costs are $15 per hour for test device 1, $12 per hour for test device 2, $18 per hour for test device 3. Quitmeyer Electronics want to maximize its profits. (a) Formulate this problem as an LP problem. (b) Solve the problem by using QM for Windows. What is the best product mix? (c) What is the value of an additional minute of time per week on test device 1? Test device 2? Test device 3? Should Quitmeyer Electronics add more test device time? If so, on which equipment?

1

Part A)

Formulate this problem as an LP problem.
PROFIT = REVENUETOTAL - MATERIALSTOTAL - LABOURTOTAL

MAXIMIZE PROFIT: REVENUETOTAL

= I(200$) + E(120$) + C(180$) + F(130$) + H(430$) + M(260$)

MATERIALSTOTAL = I(35$) + E(25$) + C(40$) + F(45$) + H(170$) + M(60$) LABOURTOTAL = LCUNIT(I)*I + LCUNIT(E)*E + LCUNIT(C)*C + LFUNIT(F)*F + LCUNIT(H)*H + LCUNIT(M)*M = 3.65(I) + 2.05(E) + 4.50(C) + 2.50(F) + 10.20(H) + 8.25(M) WHERE: T LCUNIT(I)*I 3.65 LCUNIT(I)*E 2.05 LCUNIT(I)*C 4.50 LCUNIT(I)*F 2.50 LCUNIT(I)*H 10.20 LCUNIT(I)*M 8.25 AND : Td1 = = = = = = = = = = = = = = time in minutes/60 T1I(15) + T2I(12) + T3I(18) .117(15) + .033(12) + .083(18) T1I(15) + T2I(12) + T3I(18) .050(15) + .083(12) + .017(18) T1C(15) + T2C(12) + T3C(18) .200(15) + .050(12) + .050(18) T1F(15) + T2F(12) + T3F(18) .100(15) + .033(12) + .033(18) T1H(15) + T2H(12) + T3H(18) .300(15) + .250(12) + .150(18) T1M(15) + T2M(12) + T3M(18) .283(15) + .283(12) + .033(18)

TDEVICE1/60 of I * # of I TDEVICE1/60 of E * # of E TDEVICE1/60 of C * # of C TDEVICE1/60 of F * # of F TDEVICE1/60 of H * # of H TDEVICE1/60 of M * # of M + Td1 = .117(I) + .050(E) + .200(C) + .100(F) + .300(H) + .283(M) TDEVICE2/60 of I * # of I TDEVICE2/60 of E * # of E TDEVICE2/60 of C * # of C TDEVICE2/60 of F * # of F TDEVICE2/60 of H * # of H TDEVICE2/60 of M * # of M + Td2 = .033(I) + .083(E) + .050(C) + .033(F) + .250(H) + .283(M) TDEVICE3/60 of I * # of I TDEVICE3/60 of E * # of E TDEVICE3/60 of C * # of C TDEVICE3/60 of F * # of F TDEVICE3/60 of H * # of H TDEVICE3/60 of M * # of M + Td3 = .083(I) + .017(E) + .050(C) + .033(F) + .150(H) + .033(M)

Td2

=

Td3

=

Given time in minutes is converted to hours (being in a managerial business I calculate labour cost by the hour or ¼ hour not minute)

2

LINEAR PROGRAM MODEL: OBJECTIVE: PI(I) + PE(E) + PC(C) + PF(F) + PH(H) + PM(M) 161.35(I) + 92.95(E) + 135.50(C) + 82.50(F) + 249.80(H) + 191.75(M) CONSTRAINTS: Td1 or .117(I) + .050(E) + .200(C) + .100(F) + .300(H) + .283(M) ≤ 120 Td2 or .033(I) + .083(E) + .050(C) + .033(F) + .250(H) + .283(M) ≤ 120 Td3 or .083(I) + .017(E) + .050(C) + .033(F) + .150(H) + .033(M) ≤ 100

AND:

I,E,C,F,H,M ≥ 0

PART B) Solve the problem by using Excel/Solver. What is the best product mix?
Solved! – see attached reports and XLS working spreadsheet (this was a dooooooosy!) Best Product Mix – Make 496.55 (rounded to 497) units of Internal Modems and 1241.38 (rounded to 1242) units of Eternal Modems for a profit of $195504.83

PART C-1) What is the value of an additional minute of time per week on test device 1?
21.41$ or the shadow price (in hours / 60) 1284.52/60 = 21.41

PART C-2) What is the value of an additional minute of time per week on test device 2?
5.74$ or the shadow price (in hours / 60) 344.69/60 = 5.74

PART C-3) What is the value of an additional minute of time per week on test device 3?
Since shadow price is 0, value of any additional minute to TD3 is also 0.00$

PART C-4) Should Quitmeyer Electronics add more test device time? If so, on which equipment?
Due to the fact that the shadow price of TD1 and TD2 are greater than ( > ) 0, quitmeyer should add more test time here to TD1 and TD2 not on TD3.

3

Microsoft Excel 12.0 Sensitivity Report Worksheet: [Robbie Parker - DS2casestudy.problem 8-12 page 324.xlsx]quitmeyer- 8.12 page 324 Report Created: 2014-04-28 22:47:45

Adjustable Cells Cell $B$13 $C$13 $D$13 $E$13 $F$13 $G$13 Name Solution value Internal modems Solution value External modems Solution value Circuit boards Solution value Floppy drives Solution value Hard drives Solution value Memory boards Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 496.55 0.00 161.35 55.53333333 69.40833333 1241.38 0.00 92.95 310.425 23.8 0.00 -138.64 135.5 138.637931 1E+30 0.00 -57.44 82.5 57.44137931 1E+30 0.00 -221.73 249.8 221.7275862 1E+30 0.00 -269.86 191.75 269.8586207 1E+30

Constraints Cell Name $H$19 Test device 1 $H$20 Tets device 2 $H$21 Test device 3 Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 120.00 1284.52 120 47.82608696 48 120.00 344.69 120 80 85.71428571 62.07 0.00 100 1E+30 37.93103448

Microsoft Excel 12.0 Answer Report Worksheet: [Robbie Parker - DS2casestudy.problem 8-12 page 324.xlsx]quitmeyer- 8.12 page 324 Report Created: 2014-04-28 22:47:45

Target Cell (Max) Cell $H$17 Profit

Name

Original Value $195,504.83

Final Value $195,504.83

Adjustable Cells Cell Name $B$13 Solution value Internal modems $C$13 Solution value External modems $D$13 Solution value Circuit boards $E$13 Solution value Floppy drives $F$13 Solution value Hard drives $G$13 Solution value Memory boards

Original Value 496.55 1241.38 0.00 0.00 0.00 0.00

Final Value 496.55 1241.38 0.00 0.00 0.00 0.00

Constraints Cell Name $H$19 Test device 1 $H$20 Tets device 2 $H$21 Test device 3

Cell Value Formula Status Slack 120.00 $H$19…...

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