3 Before a new product can be introduced, the activities in Table 40 must be completed (all times are in weeks).

a Draw the project diagram.
b Determine all critical paths and critical activities.
c Determine the total float and free float for each activity.
d Set up an LP that can be used to determine the critical path.
e Formulate an MCNFP that can be used to find the critical path.
f It is now 12 weeks before Christmas. What is the probability that the product will be in the stores before Christmas?
g The duration of each activity can be reduced by up to 2 weeks at the following cost per week: A, $80; B, $60; C, $30; D, $60; E, $40; F, $30; G, $20. Assuming that the duration of each activity is known with certainty, formulate an LP that will minimize the cost of getting the product into the stores by Christmas.

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TABLE 40 m 65323442 Activity Description A Design the product B Survey the market 65 C Place orders for raw materials A 3 D Receive raw materials C E Build prototype of product A, D 3 F Develop ad campaign B G Set up plan for mass production E H Deliver product to stores G, F Predecessors Duration a b 2 4 564 2 0 4 2421320 10 6 4 3 5