Question $1$:

A company is considering implementing a just$-$in$-$time $($JIT$)$ inventory system. Which of the following is the MOST important factor to consider before implementing JIT?

$($a$)$ The company's lead times for obtaining raw materials

$($b$)$ The company's ability to forecast demand accurately

$($c$)$ The company's supplier relationships

$($d$)$ The company's production capacity

$($e$)$ All of the above

Question $2$:

A company is trying to improve the efficiency of its assembly line. Which of the following techniques would be MOST effective in reducing waste and improving throughput?

$($a$)$ Value stream mapping

$($b$)$ Statistical process control

$($c$)$ Total quality management

$($d$)$ Lean manufacturing

$($e$)$ All of the above

Question $3$:

A company is experiencing a high rate of product returns due to defects. Which of the following quality control techniques would be MOST effective in reducing defects?

$($a$)$ Poka$-$yoke

$($b$)$ Quality control circles

$($c$)$ FMEA $($Failure Mode and Effects Analysis$)$

$($d$)$ Six Sigma

$($e$)$ All of the above

Question $4$:

A company is trying to reduce its supply chain costs. Which of the following strategies would be MOST effective in reducing costs?

$($a$)$ Vendor consolidation

$($b$)$ Strategic sourcing

$($c$)$ Global sourcing

$($d$)$ E$-$procurement

$($e$)$ All of the above

Question $5$:

A company is trying to improve its customer service. Which of the following initiatives would be MOST effective in improving customer satisfaction?

$($a$)$ Implementing a CRM $($Customer Relationship Management$)$ system

$($b$)$ Reducing the time to resolve customer complaints

$($c$)$ Providing more self$-$service options for customers

$($d$)$ All of the above

Sure, here are $5$ option$-$based questions of advanced math:

$**$Question $1$:$**$

Find the derivative of the following function:

$```$

f$($x$)=$ e$^(2$x$)+$ sin$(3$x$)$

$```$

$**$Options:$**$

$($a$)2$e$^(2$x$)+3$cos$(3$x$)$

$($b$)4$e$^(2$x$)+9$sin$(3$x$)$

$($c$)2$e$^(2$x$)+3$xcos$(3$x$)$

$($d$)4$e$^(2$x$)+9$xsin$(3$x$)$

$($e$)$ None of the above

$**$Question $2$:$**$

Evaluate the following integral:

$```$

$($x$^2+3$x $+2)$ dx

$```$

$**$Options:$**$

$($a$)($x$^3+3$x$^2+2$x$)+$ C

$($b$)($x$^3+3$x$^2+2)+$ C

$($c$)($x$^3+3$x$^2+1)+$ C

$($d$)($x$^3+3$x $+1)+$ C

$($e$)$ None of the above

$**$Question $3$:$**$

Find the solution to the following differential equation:

$```$

dy$/$dx $=$ y $+$ x

$```$

$**$Options:$**$

$($a$)$ y $=$ C$*$e$^($x$)$

$($b$)$ y $=$ C$*$e$^(-$x$)$

$($c$)$ y $=$ C$*$x $+1$

$($d$)$ y $=$ C$/($x $+1)$

$($e$)$ None of the above

$**$Question $4$:$**$

Find the eigenvalues of the following matrix:

$```$

A $=[[2,1],[3,4]]$

$```$

$**$Options:$**$

$($a$)1,5$

$($b$)2,3$

$($c$)1,4$

$($d$)2,4$

$($e$)$ None of the above

$**$Question $5$:$**$

Find the inverse of the following matrix:

$```$

B $=[[1,2],[3,4]]$

$```$

$**$Options:$**$

$($a$)[[-1,2],[3,-1]]$

$($b$)[[1/2,-1/2],[-3/2,1/2]]$

$($c$)[[1/2,-1],[-3,2]]$

$($d$)[[1,2],[-3,4]]$

$($e$)$ None of the above