Solutions

Single Period Linear Programming – Review Problems

ExcelSolutions

  1. Classic
    Define: S - the number of Santa candles produced

C - the number of Christmas trees candles produced
G - the number of Gingerbread house candles produced

The model:

Max 16S + 9C + 27G

s.t

.10S + .10C + .25G <= 21 (Molding)

.35S + .15C + .40G <= 63 (Decorating)

.08S + .03C + .05G <= 21 (Packaging)

From Excel we have: S = 154.73; C = 0; G = 22.10; Profit = $3072.63

Resource used: Molding in full; Decorating in full; Packaging13.48 days (7.52 days remain unused).

2.Rozac

Define: X1, X2, X3, and X4 – how many pounds of each chemical are used

A, B, and C – how many pounds of each active ingredient are included in the drug

The model:

Min 8X1 + 10X2 + 11X3 + 14X4

s.t.

X1 + X2 + X3 + X4= 1000
.03X1 + .06X2 + .10X3 + .12X408(1000) = 80
.02X1 + .04X2 + .03X3 + .09X4.04(1000) = 40

.01X1 + .01X2 + .04X3 + .04X4.02(1000) = 20

X3300

X1 + X2320

3.Floataway

Define: X1, X2, X3, and X4 – the number of “Speedhawks”, “Silverbirds”, “Catmans”,and “Classy” boats built respectively.

The model:

Max 70X1 + 50X2 + 80X3 + 110X4

s.t.

6000X1 + 7000X2+ 5000X3 + 9000X4 400,000

X1 + X2 + X3 + X450

X1 + X2 = X3 + X4

X1 – X320and X3 – X120

3X1 + 5X2 + 2X3 + 6X4200

  1. WOE

MGR, ENG, TECH, OTHR – represent the number of managers, engineers, technicians, and others left after the manpower reduction takes place.

The model:

Min (1280+320) MGR + 800ENG + 600TECH + (10+245) OTHR

s.t.

MGR 90; ENG 3000; TECH 

ENG + TECH 5(MGR + OTHR)

2(6000 – ENG + 3000 – TECH)  150 – MGR + 900 – OTHR

1280MGR + 245OTHR .10(320MGR + 300ENG + 600TECH + 10OTHR)