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13. Here is a list of activity times for a project as well as crashing costs for its activities. Determine which activities should be crashed and the total cost of crashing if the goal is to shorten the proj- ect by three weeks as cheaply as possible. First construct a network diagram. You can use either an AOA or an AON (see Example 5). Path Activity Duration (weeks) ) First Crash Second Crash Top A 5 $8 $10 B 6 7 9 3 14 15 Middle D 3 9 11 E 7 8 9 3 15 Bottom F 5 15 G 5 11 13 H 5 14 ITMO 10 12 14 8. The parts department of a large automobile dealership has a counter used exclusively for mechan- ics' requests for parts. The time between requests can be modeled by a negative exponential dis- tribution that has a mean of five minutes. A clerk can handle requests at a rate of 15 per hour, and this can be modeled by a Poisson distribution that has a mean of 15. Suppose there are two clerks at the counter a. On average, how many mechanics would be at the counter, including those being served? 5. What is the probability that a mechanic would have to wait for service! c. If a mechanic has to wait, how long would the average wait be? d. What percentage of time are the clerks idle? e. F clerks represent a cost of $20 per hour and mechanics a cost of $30 per hour, what number of clerks would be optimal in terms of minimizing total cost? . The manager of the deli section of a grocery superstore has just learned that the department has 112 pounds of mayonnaise, of which 70 pounds is approaching its expiration date and must be used. To use up the mayonnaise, the manager has decided to prepare two items: a ham spread and a deli spread. Each pan of the ham spread will require 1.4 pounds of mayonnaise, and each pan of the deli spread will require 1.0 pound. The manager has received an order for 10 pans of ham spread and 8 pans of the deli spread. In addition, the manager has decided to have at least 10 pans of each spread available for sale. Both spreads will cost $3 per pan to make, but ham spread sells for $5 per pan and deli spread sells for $7 per pan. a. Determine the solution that will minimize cost. b. Determine the solution that will maximize profit