Quantitative Analysis 3.37

3.37

a.

Decision Variables:

XiF: Number of tons of commodity 1 to be placed in Forward position of Cargo Ship

XiC: Number of tons of commodity 2 to be placed in Center position of Cargo Ship

XiR: Number of tons of commodity 3 to be placed in Rear position of Cargo Ship

Where i=1-4

Maximize 70(X1F+X1C+X1R) + 50(X2F+X2C+X2R) + 60(X3F+X3C+X3R) + 80(X4F+X4C+X4R)

Subject to:

X1F+X1C+X1R < 4800 (total amount of commodity 1 available to be shipped)

X2F+X2C+X2R < 2500 (total amount of commodity 2 available to be shipped)

X3F+X3C + X3R < 1200 (total amount of commodity 3 available to be shipped)

X4F+X4C+X4R < 1700 (total amount of commodity 4 available to be shipped)

X1F+X2F+X3F+X4F < 3000 (weight capacity in tons for forward hold)

X1C+X2C+X3C+X4C < 6000 (weight capacity in tons for center hold)

X1R+X2R+X3R+X4R < 4000 (weight capacity in tons for rear hold)

40X1F+25X2F+60X3F+55X4F < 145000 (volume capacity in ft3 for forward hold)

40X1C+25X2C+60X3C+55X4C < 180000 (volume capacity in ft3 for center hold)

40X1R+25X2R+60X3R+55X4R < 155000 (volume capacity in ft3 for rear hold)

X1F+X2F+X3F+X4F > .9(X1R+X2R+X3R+X4R)

X1F+X2F+X3F+X4F < 1.1(X1R+X2R+X3R+X4R)

X1C+X2C+X3C+X4C > .4(X1F+X1C+X1R+X2F+X2C+X2R+X3F+X3C+X3R

+X4F+X4C+X4R)

X1C+X2C+X3C+X4C < .6(X1F+X1C+X1R+X2F+X2C+X2R+X3F+X3C+X3R

+X4F+X4C+X4R)

all > 0

b.

c. Profit = $669,000

| 1 | 2 | 3 | 4 |

Forward | X11=1287.5 | X21=0 | X31=0 | X41=1700 |

Center | X12=1580 | X22=2500 | X32=0 | X42=0 |

Rear | X13=1932.5 | X23=0 | X33=1200 | X43=0 |