# carly jones, a current mba student, decides to spend her summer designing and marketing bicycling maps of the dc metro area. she has designed 4 maps, corresponding to different areas in and around the

## Project Description:

1. (12 points) carly jones, a current mba student, decides to spend her summer designing and marketing bicycling maps of the dc metro area. she has designed 4 maps, corresponding to different areas in and around the city. the maps differ in size, colors used, and complexity of the topographical relief (showing hills and valleys). she has retained a printer to produce the maps. each map must be printed, cut, and folded. the time (in seconds) to do this for the four types of maps is:
map print cut fold
a 1 2 3
b 2 4 2
c 3 1 5
d 3 3 3
available 15000 20000 20000
the printer has a limited amount of time in his schedule, as noted in the table.
the profit per map, based on the projected selling price minus printers cost and other variable cost, comes out to approximately \$1 for a and b and \$2 for c and d. in order to have a sufficiently nice display, at least 1000 of each type must be produced.
this gives the formulation: max a + b + 2 c + 2 d
subject to
a + 2 b + 3 c + 3 d _= 15000
2 a + 4 b + c + 3 d _= 20000
3 a + 2 b + 5 c + 3 d _= 20000
a _= 1000
b _= 1000
c _= 1000
d _= 1000
attached is the solver output.
final reduced objective allowable allowable
cell name value cost coefficient increase decrease
\$b\$11 xa 1500 0 1 1 0.333333
\$b\$12 xb 1000 0 1 0.333333 1e+30
\$b\$13 xc 1000 0 2 0.333333 1e+30
\$b\$14 xd 2833.333 0 2 1 0.5

constraints
final shadow constraint allowable allowable
cell name value price r.h. side increase decrease
\$b\$17 print 15000 0.5 15000 100 366.6667
\$b\$18 cut 16500 0 20000 1e+30 3500
\$b\$19 fold 20000 0.166667 20000 7000 1000
\$b\$20 mina 1500 0 1000 500 1e+30
\$b\$21 minb 1000 -0.333333 1000 1750 1000
\$b\$22 minc 1000 -0.333333 1000 500 1000
\$b\$23 mind 2833.333 0 1000 1833.333 1e+30
answer the following questions:

a) the marketing analysis on map d is still incomplete, though it is known that the profit of \$2 per item is within \$.25 of the correct value. it will cost \$500 to complete the analysis. should carly continue with the analysis?

b) how much is carly willing to pay for extra printing time? cutting time? folding time? for each, how much extra time are we willing to buy at that price?

c) suppose we reduced the 1000 limit on one item to 900. which map should be decreased, and how much more would carly make?

d) a fifth map is being thought about. it would take 2 minutes to print, 2 minutes to cut, and 3 minutes to fold. what is the least amount of profit necessary in order to consider producing this map?
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Price Type: Negotiable

Completed
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