PROBLEM $-5)(20$ Pts$.)$ The XYZ Company is manufacturing PRS products. There are $5$ jobs on three stations for

the production of an PRS product. Assume that the jobs are processed in the sequence X$-$Y$-$Z$.$ The production

engineer uses a kanban system. On average the firm produces $5,000$ PRS products monthly. Production lead time is

$3$ days, and the firm plans to have $15$ percent buffer stock. Assume that there are $20$ working days per month.

Use the information above to solve the following problems.

a$.(3$ Pts$.)$ If each container holds $25$ PRS products, what is the total number of kanban tickets required?

b$.(3$ Pts$.)$ What is the maximum on$-$hand inventory of the PRS products the company can expect to have using

the kanban system?

c$.(7$ Pts$.)$ Find the optimal sequencing of the jobs in order to minimize the makespan. What is the makespan

at the optimal solution?

d$.(7$ Pts$.)$ Draw a Gantt chart illustrating your optimal sequencing solution.