This course for Quantitative Methods in Engineering ManagemenProblem $4.$ The Albaik Restaurant is open $24$ hours a day. Kitchen staff show for work at $3$ a$.$m$.,$

$7$ a$.$m$.,11$ a$.$m$.,3$ p$.$m$.,7$ p$.$m$.,$ or $11$ p$.$m$.,$ and each shift lasts for $8-$hour. The following table

shows the minimum number of workers needed during the six periods into which the day is

divided. Albaik's scheduling problem is to determine how many staff should report for work at the

start of each time period to minimize the total staff required for one day's operation.

Q$1.$ Set up the objective function and constraints of this problem using LP so that the total number

of staffs needed is minimized $(15$ pts $)$

Q$2.$ Solve the problem and provide the optimal solution. $(15$pts$)$