#3) A new car dealership has full time sales people and part time salespeople th
ID: 3293143 • Letter: #
Question
#3)
A new car dealership has full time sales people and part time salespeople that work on Sundays.“Working” is considered when the salespeople are with customers.On Sundays, the full time sales people work six hours and also have a one hour lunch break and attend a one hour meeting.Part time people work four consecutive hours with customers, with no lunch and no meetings to attend. Full time workers must work at least 60% of total hours demanded on Sunday.No part time workers can work the first hour.
Full time workers make $200 a day and part time workers make $64 dollars a day.
30% of full time employees go to lunch from 1:00 to 2:00 and 70% go from 2:00 to 3:00.
50% of full time employees go to the meeting from 10:00 to 11:00 and 50% go from 3:00 to 4:00.
Find the minimum cost of the car dealership to staff Sundays that meets or exceeds demand and satisfies all constraints.
TimeDemand
10:00 to 11:004
11:00 to 12:008
12:00 to 1:0013
1:00 to 2:0015
2:00 to 3:0010
3:00 to 4:009
4:00 to 5:0014
5:00 to 6:0010
Explanation / Answer
Solution
Preparatory work
Since a full-timer is paid $200 per day and a part-timer is paid is paid $64 per day, in terms of cost, one full-timer = 3.125 part-timer. …………………………………………………..(1)
Since, in the first hour (10 to 11), no part-timer is available and 50% full-timers are in meeting, to meet demand of 4, minimum of 8 full-timers is necessary. ………..(2)
The given data and further working are given in the following table assuming 8 and 9 full-timers.
[D: Demand; F: # Full-timers available; P: # Additional Part-timers required
Time Slot
D
8 full-timers
9 full-timers
F
P
F
P
10 to 11
4
50% of 8 = 4 (*1)
0
4
0
11 to 12
8
8
0
9
0
12 to 1
13
8
5
9
4
1 to 2
15
70% of 8 = 5 (*2)
10
6
9
2 to 3
10
30% of 8 = 2 (*2)
8
2
8
3 to 4
9
50% of 8 = 4 (*1)
5
4
5
4 to 5
14
8
6
9
5
5 to 6
10
8
2
9
1
Total cost ($)
(8 x 200) + (10 x 64) = 2240
(9 x 200) + (9 x 64) = 2376
*1 taking into account percentage attending meeting
*2 taking into account percentage going for lunch
Since as the number of F increases cost increases, optimum decision would be to have 8 F and 10 P (5 from 12 to 4 and 5 from 1 to 5) with a resultant total cost of $2240. DONE
Time Slot
D
8 full-timers
9 full-timers
F
P
F
P
10 to 11
4
50% of 8 = 4 (*1)
0
4
0
11 to 12
8
8
0
9
0
12 to 1
13
8
5
9
4
1 to 2
15
70% of 8 = 5 (*2)
10
6
9
2 to 3
10
30% of 8 = 2 (*2)
8
2
8
3 to 4
9
50% of 8 = 4 (*1)
5
4
5
4 to 5
14
8
6
9
5
5 to 6
10
8
2
9
1
Total cost ($)
(8 x 200) + (10 x 64) = 2240
(9 x 200) + (9 x 64) = 2376
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