: During one eight$-$hour shift, $600$ non$-$defective parts are desired from a fabrication operation. The

standard time for the operation is $15$ minutes. Because the machine operators are unskilled, the actual

time it takes to perform the operation is $20$ minutes, and, on average, one$-$fourth of the parts that begin

fabrication are scrapped. Assuming that each of the machines used for this operation will not be

available for one hour of each shift, determine the number of machines required. $6$pts

Q$2$: In Example $2\mathrm{.}7$ solved in class, the machine fraction became $2\mathrm{.}67$ and $2$ machine per operator was

the optimum assignment. Co $=$$$15$ per hour. Suppose the cost per machine hour $($Cm$)$ is unknown. For

what range of values of Cm will the optimum assignment remain the same $(2$ machines per operator$)?$

Justify your answer. $6$pts

Q$3$: It takes $3$ minutes to load and $2$ minutes to unload a machine. Inspection, packing, and travel

between machines totals one minute. Machines run automatically for $20$ minutes. Operators cost $$12$

per hour; machines cost $$30$ per hour. $6$pts

a$.$ What is the maximum number of machines that can be assigned to an operator without

creating machine idle time during a repeating cycle?

b$.$ What assignment minimizes the cost per unit produced?

c$.$ If four machines are assigned to an operator, what will be the cost per unit produced?

d$.$ For what range of values for concurrent activity is the optimum assignment equal to four?

Q$4$: An industrial engineer is asked to propose a facilities layout for a manufacturing firm. He is

supposed to use prioritization matrix to prioritize his alternatives and propose the best alternative.

Based on the manager$$s decision he has to focus on $4$ criteria. After a detailed analysis the

following prioritizing matrix of criteria has been generated. $6$pts

Where A$,$ B$,$ C and D are the criteria to design a layout and the numbers are weights used to

compare criteria. $($The weights definition is the same as lecture $8).$ He also has generated $3$

layouts P$,$ Q and R alternatives and the prioritizing matrix of layouts for each criterion is as

follow:

Rank the alternatives based on the criteria.

Q$5$: Use Direct Clustering Algorithm to arrange the machines and parts in the machine$-$part matrix

below to the manufacturing cells. If there are bottleneck machines, decide what you can do$.6$pts