Case Study $4$: Productivity

$($I$)$ JACON Limited produces glass bottles for use in a local beverage company. Currently, JACON produces $1600$ cases of bottles per day. The $20$ workers at ALLISON Products work from $7$ a$.$m$.$ until $4$ p$.$m$.,$ with $30$ minutes off for lunch and a $15-$minute break during the morning work session and another at the afternoon work session. JACON is in the competitive packaging industry and needs to increase productivity to stay competitive. They feel that a $20$ percent increase is needed. JACON's management believes that the $20$ percent increase will not be possible without a change in working conditions, so they change work hours. The new schedule calls on workers to work from $7$:$30$ a$.$m$.$ until $4$:$30$

p$.$m$.,$ during which workers can take one hour off at any time of their choosing. Obviously, the number of paid hours is the same as before, but production increases, perhaps because workers are given a bit more control over their workday. After this change, bottle production increased to $1800$ cases of bottles per day.

Required:

a$)$ Calculate labor productivity for the initial situation $[4$ marks$]$

b$)$ Calculate labor productivity for the hypothetical $20$ percent increase $[4$ marks$]$

c$)$ What is the productivity after the change in work rules? $[3$ marks$]$

d$)$ Write a short paragraph analyzing these results. $[4$ marks$]$

$($II$)$ MetalCraftJa produces a special type of metal mini$-$chairs, which are used mostly by Basic$/$Infant schools in the parish of St Catherine. Current operations allow the welding assembly to make $550$ mini$-$chairs per day, in two $8-$hour shifts $(275$ mini$-$chairs per shift$).$ MetalCraftJa has introduced some moderate changes in equipment, and conducted appropriate job training, so that production levels have risen to $325$ mini$-$chairs per shift. Labor costs average $$10$ per hour for each of the $5$ full$-$time workers on each shift. Capital costs were previously $$3,000$ per day, and rose to $$3,200$ per day with the equipment modifications. Energy costs were unchanged by the modifications, at $$400$ per day.

a$)$ What is the firm's multifactor productivity before the changes? $(5$ marks$)$

b$)$ What is the firm's multifactor productivity after the changes? $(5$ marks$)$

Case Study $5$: Inventory Management.

I$)$ A Furniture manufacturing company uses $1200$ units of an item annually and the cost price is $$250$ per unit. The ordering costs are $$600$ per order and holding costs are $$4\mathrm{.}00$ per item per annum.

Required:

a$)$ Calculate The economic order quantity.

b$)$ Determine the number of orders per annum

c$)$ Determine the annual stock holding cost

$(3$ marks$)$

d$)$ Determine the annual ordering cost

$(2$ marks$)$

$(2$ marks$)$

$(3$ marks$)$

$($II$)$ A regional distributor purchases discontinued appliances from various suppliers and then sells them on demand to retailers in the region. The distributor operates $5$ days per week, $52$ weeks per year. Only when it is open for business can orders be received. Management wants to reevaluate its current inventory policy, which calls for order quantities of $440$ counter$-$top mixers. The following data are estimated for the mixer: