using excel, The PDA market has proliferated into a spectrum of products over the last

decade, with each new product outdoing the previous in size, performance, or both.

Consumers rarely pay the fair price for producing a PDA, as PDAs are often offered

as part of a wireless contract with a data provider. Data providers purchase PDA units

in bulk from the manufacturer, and resell them $($as part of the data service contract$)$

at or below the prices paid to the PDA manufacturer. Therefore, data providers are

the direct buyers of PDAs with consumers being the end users. Manufacturers of

PDAs offer a breadth of products to meet various price and functionality points and

permit the data providers flexibility in pricing.

Manufacturers of PDAs compete for exclusive or preferred agreements with

data providers. The PDA production technology requires many components sourced

from scores of vendors in many countries. Most assembly is conducted in China and

South East Asia. Managing the production of PDAs and controlling for shocks in the

supply chain are main concerns for manufacturers of PDAs.

The ASCO company manufactures two PDA models, Hyper and Zeon. Each is

up$-$scale and offers rather advanced features popular in the US market. These PDAs

are not sold directly to consumers, but rather under contract to data providers. Each

Hyper PDA sells for $$300$ and each Zeon PDA sells for $$250.$ That is to say, that ASCO

receives those respective prices from the data providers buying the PDAs. ASCO

purchases electrical, memory and other components for each Hyper PDA for $$260.$

Similar components for a Zeon PDA cost $$190.$

Production of each model involves three major processes: circuit board

fabrication, touch$-$control screen construction, and case installation in conjunction

with final assembly. ASCO prides itself on high$-$quality touch screen and has

developed a new technology for touch recognition. Circuit board fabrication is largely

driven by the use of a licensed technology for board cutting and memory integration.

ASCO does not consider its circuit board process any more advanced than others in

the industry. There are two separate and completely automated lines for circuit

board fabrication, one dedicated to Hypers and one to Zeons. This split operation is

in part a residue of two separate divisions from a previous organization of the

enterprise. Due to the disparate cost in labor and the need for human activity in some

of the circuit board fabrication, the company has even considered outsourcing these

processes or at least consolidating the two into one circuit board fabrication facility.

The head office has, however, recommended that the two lines remain independent

for now to allow for fabrication to continue in the event that one line is inoperable.

However, the touch screen construction and case assembly departments are shared

in the production of the two PDA lines. Given the proprietary nature of the touch

screen technology, its assembly is kept controlled in an ASCO$-$owned facility. Case

installation and assembly stage not only ensures a tough product for consumer use

but also allows for final quality control.

The capacity of the Hyper circuit board fabrication line is $70$ PDAs per day,

while that of the Zeon line is $50$ PDAs per day. The touch$-$enabled screen department

has $20$ workstations, while the case assembly department has $16$ workstations. Each

workstation can process one PDA at a time and is operated $6$ hours a day. Each Hyper

PDA takes $1$ hour in screen production and $1$ hour for case assembly. Each Zeon PDA

requires $2$ hours for screen production and $1$ hour for case assembly.

Workers in the touch screen department and case assembly departments are

paid $$10$ an hour. Heating, lighting, and other overhead charges amount to $$1,000$

per day.

Given the highly competitive nature of the business, ASCO management would

like to make best use of the available plant capacity. Moreover, they would like to

know potential areas of expansion that would improve profitability of their

operation. Finally, they would like to understand the effect of unexpected changes

in their production process and market environment. Specifically, the management

would like to know answers to the following questions.

a$.$ How many Hypers and Zeons should ASCO produce each day? What will be

their maximum total profit?

b$.$ How should they allocate the available resources across the two models?

Where are the bottlenecks?

The PDA market is dynamic. Recent market analysis shows that Hypers are

selling well. A contract with a major data provider is coming up$.$ The CEO believes

that Hypers can yield a profit margin of $$40$ under the new contract. Still, the CEO is

prepared to lower the price on the Hyper by as much as $$10$ per PDA to keep the

contract. Consider the best case scenario of a $$20$ increase and a worst case scenario

of a $$10$ decrease in the Hyper$$s profit.

c$.$ How should the production line adju