$1.$ Draw the network using AOA convention.

$2.$ Determine the critical path, expected project completion time, and variance of the critical path.

$3.$ Landers Supermarket wants to include the following condition in the contract. The IT firm will earn a bonus of $$30,000$ if the project is completed in $30$ weeks or less. However, a penalty of $$15,000$ will be incurred if they complete the project beyond $40$ weeks. Is it advisable for the IT firm to accept the additional condition? What is the Expected Net Benefit? Explain