Question

QUESTION-1 A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in the table. Union rules state that each full-time employee must work five consecutive days and then receive two days off. The post office wants to meet its daily requirements using only full-time employees. Number of rime Employees Required Day 17 Day 2 -Tuesday Day 3-Wednesday Day 4-Thursday Day 5 Friday Day 6 Saturday Day 7 Sunday 13 15 19 14 16 Formulate the mathematical model of the problem in order to minimize the number of full-time employees that must be hired. Solve the LP using MS Excel Solver add-in

Answer 1

Decision variables: x1, x2,....x7

Let x1 be the number of workers that work from monday till friday.

x2 be the number of workers who work from tuesday till saturday.

x3 from wednesday to sunday, x4 from thurday to monday, and so on.

Objective Function:

Minimize x1+x2+x3+x4+x5+x6+x7

Constraints:

MON	X1			X4	X5	X6	X7	17
TUE	X1	X2			X5	X6	X7	13
WED	X1	X2	X3			X6	X7	15
THU	X1	X2	X3	X4			X7	19
FRI	X1	X2	X3	X4	X5			14
SAT		X2	X3	X4	X5	X6		16
SUN			X3	X4	X5	X6	X7	11

X1+X4+X5+X6+X7>=17

X1+X2+X5+X6+X7>=13

X1+X2+X3+X6+X7>=15

X1+X2+X3+X4+X7>=19

X1+X2+X3+X4+X5>=14

X2+X3+X4+X5+X6>=16

X3+X4+X5+X6+X7>=11

X1,X2,X3,X4,X5,X6,X7>=0