Case Problem: Production Strategy Managerial Report

MC506 Quantitative Methods for Managers - Start Date: July 1, 2003

Analyze the production problem at Better Fitness, Inc. and prepare a report for BFI's president presenting your findings and recommendations. Include (but donot limit your discussion to) a consideration of the following items:

1. The recommended number of BodyPlus 100 and BodyPlus 200 machines to produce.Let

BP100 = the number of BodyPlus 100 machines produced

BP200 = the number of BodyPlus 200 machines produced

Max 371BP100 + 461BP200s.t.

8BP100 + 12BP200 £ 600 hrs of machining

5BP100 + 10BP200 £ 450 hrs of painting and finishing time

2BP100 + 2BP200 £ 140 hrs of assembly, testing and packaging.

-0.25BP100 + .75BP200 ³ 0

BP100 , BP200 ³ 0

By Debbie St. George: Student #: 1086941

Optimal solution: BP100 = 50, BP200 = 50/3 or 16.667, profit = $26,233.33. See Management Science notes.

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10

20

40

30

50

60

70

80

0 10 20 30 40 50 60 70 80 90 100Number of BodyPlus 100

Num

ber

of B

odyP

lus

200

Optimal Solution

BodyPlus 200 Requirement

Painting and Finishing

Assembly, Test, and Packaging

Machining and Welding

BP100

BP200

2. The effect on profits of the requirement that the number of units of the BodyPlus 200 produced must be at least 25% of the total production.If the requirement were reduced to at least 24% of total production, the new optimal solution is BP100 = 1425/28, BP200 = 225/14, with a total profit of $26,290.18; thus, total profits would increase by $56.85. In the short run the requirement reduces profits.

3. Where efforts should be expended in order to increase profits.Retain the constraint requiring that the number of units of the BodyPlus 200 produced be at least 25% of total production.Obtain additional machining and welding time to increase profits as the current optimal solution uses the current machining and welding time.

1. The recommended number of BodyPlus 100 and BodyPlus 200 machines to produce.

hrs of painting and finishing time

hrs of assembly, testing and packaging.

= $26,233.33. See Management Science notes.

Management Science Program - LINEAR PROGRAMMING PROBLEM

MAX 371BP100+461BP200

S.T.

1) 8BP100+12BP200<600 2) 5BP100+10BP200<450 3) 2BP100+2BP200<140 4) -0.25BP100+0.75BP200>0

OPTIMAL SOLUTION

Objective Function Value = 26233.333

Variable Value Reduced Costs -------------- --------------- ------------------

Constraint Slack/Surplus Dual Prices -------------- --------------- ------------------ 1 0.000 43.722 2 33.333 0.000 3 6.667 0.000 4 0.000 -84.889

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- BP100 307.333 371.000 No Upper Limit BP200 -1113.000 461.000 556.500

RIGHT HAND SIDE RANGES

Constraint Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- 1 0.000 600.000 630.000 2 416.667 450.000 No Upper Limit 3 133.333 140.000 No Upper Limit 4 -7.500 0.000 15.000

or $26,233.33

BP100 50.000 0.000 BP200 16.667 0.000

Notes:

Department BP100 BP200Frame machining & welding time 4 hrs 5 hrs

Frame paint & finish 2 hrs 4 hrs

Press machining & welding time 2 hrs 3 hrs

Press paint & finish 1 hr 2 hrs

Pec-dec machining & welding time 2 hrs 2 hrs

Pec-dec paint & finish 2 hrs 2 hrs

Leg press machining & welding time 0 hrs 2 hrs

Leg press paint & finish 0 hrs 2 hrs

Assembly, testing and packaging 2 hrs 2 hrs

Production Time Requirements Totals for BP100 and BP200

Department BP100 BP200Machining & welding time 8 hrs * $20 = $160 12 hrs * $20 = $240Paint & finish 5 hrs * $15 = $75 10 hrs * $15 = $150Assembly, testing and packaging 2 hrs * $12 = $24 2 hrs * $12 = $ 24

15 hrs = $259 24 hrs = $414

Notes & constraints for next production period

8BP100 +5BP100 +2BP100 +

Suggested Price

BP100 $2,400 Frame 450 Press 300 Pec-dec 250 Assembly/Pack 50 Labor 259 $1,309

$1,091

Suggested Price

BP100 $3,500

Production Requirements for BP100 and BP200 Production Time

Frame 650 Press 400 Pec-dec 250 Leg press 200 Assembly/Pack 75 Labor 414 $1,989

$1,511 Max +371BP100

12BP200 £ 600 hrs of machining

10BP200 £ 450 hrs of painting and finishing time

2BP200 £ 140 hrs of assembly, testing and packaging.

Dealers 70% Price$1,680

$1,309 $371 Profit per unit for BP100

Dealers 70% Price$2,450

Production Requirements for BP100 and BP200 Production Time

$1,989 $461 Profit per unit for BP200

461BP200