Problem 2.6 (15 points) You work at a distribution center. A distribution center houses product for retail or direct-to customer. The warehouse uses a picking system to collect orders. The picking system is manual and uses employees to travel around the facility picking product based on a pick list provided at the beginning of the shift. The picking software and hardware package the facility uses has just released an update. The update comes with new mobile picking devices that are easier to hold in one hand, have less technical issue connecting to the server, and are more user friendly. Think about it like moving up from a kindle fire to an iPad. The software also has several updates including removing the manual process you perform every day to create and assigning pick sheets to employees. There is an overall cost of $15,000 for the update. This includes 20 new devices and the software update and training. The maintenance contract will be $2,500 per year for the first year and will increase by $300 each year after for 7 years. Therefore, the contract is for a total of 8 years. Each picking device is estimated to have a salvage value of $100. You can justify the benefits of an investment in many ways including revenue earned from the investment, more time available for you to do other projects, employee satisfaction, fewer picking errors, fewer part replacement, quicker picking times, etc. Each of these have a quantitative and therefore economic cost or savings.

a) What is the uniform annuity amount you would need to justify through the benefits of purchasing the upgrade? The interest rate is 9% compounded semiannually. Hint you will need to consider the maintenance contract as an arithmetic gradient. Draw the cash flow diagram to be sure you understand what the A/G equation solves for in your cash flow diagram.

b) If you can justify $6,000 in benefits per year is this enough to purchase the updated picking system?