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QUESTION

# Question 1 Giapetto's Woodcarving, Inc. manufactures two types of toys: soldiers and trains.Each soldier sold generate \$3 in profit while each train...

LP OPTIMUM FOUND AT STEP      4

OBJECTIVE FUNCTION VALUE

1)      82175.00

VARIABLE        VALUE          REDUCED COST

CPI1      3800.000000          0.000000

DAP1         0.000000          0.250000

INV       100.000000          0.000000

CPI2      3800.000000          0.000000

DAP2       300.000000          0.000000

ROW   SLACK OR SURPLUS     DUAL PRICES

2)         0.000000        -12.250000

3)         0.000000        -13.750000

4)         0.000000          2.000000

5)         0.000000          3.500000

6)       200.000000          0.000000

NO. ITERATIONS=       4

RANGES IN WHICH THE BASIS IS UNCHANGED:

OBJ COEFFICIENT RANGES

VARIABLE         CURRENT        ALLOWABLE        ALLOWABLE

COEF          INCREASE         DECREASE

CPI1       10.250000         2.000000         INFINITY

DAP1       12.500000         INFINITY         0.250000

INV        1.500000         2.000000         0.250000

CPI2       10.250000         3.500000         INFINITY

DAP2       13.750000         0.250000         2.000000

RIGHTHAND SIDE RANGES

ROW         CURRENT        ALLOWABLE        ALLOWABLE

RHS          INCREASE         DECREASE

2     3700.000000       100.000000       200.000000

3     4200.000000         INFINITY       300.000000

4     3800.000000       200.000000       100.000000

5     3800.000000       300.000000      3800.000000

6      300.000000         INFINITY       200.000000

To receive full credit You should be able to justify your answer based on the output alone without resolving the linear program.

1. What is the optimal solution including the optimal value of the objective function?
1. If the per-unit inventory cost increased from \$1.50 to \$2.50, would the optimal solution change?  Would the optimal value of the objective function change?
1. If in quarter 2 CPI’s per-seat production cost increased by \$1.25 and DAP changed its mind about the announced price increase (thus leaving it at \$12.50 per seat), would the optimal solution change?
1. If DAP reduced its per seat selling price in quarter 1 from \$12.50 to \$12.30, should CPI purchase any seats in quarter 1?
1. How much is it worth to CPI to increase its inventory capacity from 300 to 400?
1. If CPI increased its production capacity by 100 seats in both quarters 1 and 2, what would be the savings for CPI (ignoring the capacity expansion expense)?