lp solution 3-11

Greenberg Motors

Number of Units 1,276.92 476.92 1,138.46 915.38 842.31 757.69 792.31 450.00 1,000.00

Cost $10.00 $0.18 $10.00 $0.18 $11.00 $0.18 $11.00 $0.18 $6.00

Constraints:GM3A Jan balance 1 -1

GM3B Jan balance 1

GM3A Feb balance 1 1 -1

GM3B Feb balanceGM3A Mar balance 1 1 -1

GM3B Mar balanceGM3A Apr balance 1 1 -1

GM3B Apr balanceGM3A Apr Inventory 1

GM3B Apr InventoryJan storage cap 1

Feb storage cap 1

Mar storage cap 1

Apr storage cap 1

Jan labor max 1.3 0.9

Feb labor max 1.3

Mar labor max 1.3

Apr labor max 1.3

Jan labor min 1.3 0.9

Feb labor min 1.3

Mar labor min 1.3

Apr labor min 1.3

PA1 IA1 PA2 IA2 PA3 IA3 PA4 IA4 PB1

GM3A Jan prod

GM3A Jan inv

GM3A Feb prod

GM3A Feb inv

GM3A Mar prod

GM3A Mar inv

GM3A Apr prod

GM3A Apr inv

GM3B Jan prod

0.00 1,200.00 0.00 1,400.00 0.00 1,700.00 300.00

$0.13 $6.00 $0.13 $6.60 $0.13 $6.60 $0.13 $76,301.62

800.00 = 800

-1 1000.00 = 1000

700.00 = 700

1 1 -1 1200.00 = 1200

1000.00 = 1000

1 1 -1 1400.00 = 1400

1100.00 = 1100

1 1 -1 1400.00 = 1400

450.00 = 450

1 300.00 = 300

1 476.92 <= 3300

1 915.38 <= 3300

1 757.69 <= 3300

1 750.00 <= 3300

2560.00 <= 2560

0.9 2560.00 <= 2560

0.9 2355.00 <= 2560

0.9 2560.00 <= 2560

2560.00 >= 2240

0.9 2560.00 >= 2240

0.9 2355.00 >= 2240

0.9 2560.00 >= 2240LHS Sign RHS

IB1 PB2 IB2 PB3 IB3 PB4 IB4

GM3B Jan inv

GM3B Feb prod

GM3B Feb inv

GM3B Mar prod

GM3B Mar inv

GM3B Apr prod

GM3B Apr inv

R6

All entries in column R are computed using the SUMPRODUCT function.

S30

Solver includes three entries: One for each type of constraints <=, >=, and =.

Greenberg Motors (Alternate Model)

Beginning inv 0.00 476.92 915.38 757.69 0.00 0.00 0.00 0.00Production 1,276.92 1,138.46 842.31 792.31 1,000.00 1,200.00 1,400.00 1,700.00Demand 800.00 700.00 1000.00 1100.00 1000.00 1200.00 1400.00 1400.00Ending inv 476.92 915.38 757.69 450.00 0.00 0.00 0.00 300.00

Total inv Sign Cap Needed Min (>=) Max (<=)Jan storage 476.92 <= 3300 Jan labor 2,560.00 2240 2560Feb storage 915.38 <= 3300 Feb labor 2,560.00 2240 2560Mar storage 757.69 <= 3300 Mar labor 2,355.00 2240 2560Apr storage 750.00 <= 3300 Apr labor 2,560.00 2240 2560

Have Sign NeedGM3A Apr inv 450.00 = 450GM3B Apr inv 300.00 = 300

Prodn cost $10.00 $10.00 $11.00 $11.00 $6.00 $6.00 $6.60 $6.60Inv cost $0.18 $0.18 $0.18 $0.18 $0.13 $0.13 $0.13 $0.13

Total Cost =

PA1 PA2 PA3 PA4 PB1 PB2 PB3 PB4

GM3A January

GM3A February

GM3A March

GM3A April

GM3B January

GM3B February

GM3B March

GM3B April

C5

Beginning inventory in February = Ending inventory in January

I6

Only decision variables are the production quantities.

A8

Ending inventories are not decision variables in this implementation.

B8

Ending inventory = Begin inventory + Production - Demand

I8

Must ensure in Solver that ending inventories >= 0 .

$75,794.62$507.00

$76,301.62

J20

The SUMPRODUCT function is used to compute cells J20 & J21.

J22

Total cost is the same as that in Screenshot 3-11A.

lp solution 3-11

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