Problem $4$: Project Management and Quantity Discount Inventory Problems

Problem $4$A: A Small Project Management Problem

You are working on a project that has $12$ activities and you want to perform a PERT analysis on the project. You determine that the critical path consists of only five activities. You then compute the variances for the five critical activities and these variances are $3,4,2,1,$ and $6$ days.

If the desired completion date for the project is $50$ days, and the expected completion date for it $($the project$)$ is $40$ days, what is the probability that the project completion time will not be more than the desired completion date?

Problem $4$B: Quantity Discount Inventory Problem

A company will begin stocking remote control devices. The expected monthly demand is $800$ units. The controllers can be purchased from either supplier A or supplier B$.$ Their price lists are as follows:

SUPPLIER A SUPPLIER B

Quantity Unit Price Quantity Unit Price

$1199$ $$14\mathrm{.}001149$ $$14\mathrm{.}10$

$200-49913\mathrm{.}80150-34913\mathrm{.}90$

$500+13\mathrm{.}60350+13\mathrm{.}70$

The ordering cost is $$40$ and the annual holding cost is $25$ percent of the unit price. Which supplier should be used and what order quantity is optimal if the intent is to minimize total annual cost?