Problem 1
Larkin Industries has an order for 1200 door lock units from a condo developer. Each lock unit consists of 3 components: the knob and face plate, the actual lock itself, and a set of two keys. Although the processes used in the manufacture of the three components vary, there are three areas where the production manager is concerned about the availability of resources. These 3 areas, their usage by the 3 components, and availability are shown. Larkin does not have enough resources to fill this contract. A subcontractor, who can make an unlimited number of each of the three components, quotes prices below.
Resource
Knob and Plate
Lock
Key (each)
Available
Brass Alloy
12
5
1
15000 units
Machining
18
20
10
36000 minutes
Finishing
15
5
1
12000 minutes
Component
Subcontractor Cost
Larkin Cost
Knob and Plate
10.00
6.00
Lock
9.00
4.00
Keys (set of 2)
1.00
.50
(a)Develop a LP model that would tell Larkin how to fill the order for 1200 lock sets at the minimum cost.
My Solution:
Let
PM = the number of knob and plate units to make
PB = the number of knob and plate units to buy
LM = the number of lock units to make
LB = the number of lock units to buy
KM = the number of key sets to make
KB = the number of key sets to buy
Min
6PM + 10PB + 4LM + 9LB + .5KM + 1KB
s.t.
12PM + 5LM + 2KM ? 15000
18PM + 20LM + 20KM ? 36000
15PM + 5LM + 2KM ? 12000
PM + PB ? 1200
LM + LB ? 1200
KM + KB ? 1200, PM, PB, LM, LB, KM, KB ? 0
(b) Are there any unused resources, if yes which one? What is the amount of money spent purchasing components from Subcontractor? What is the range for the machining time for which its dual price will remain at the current value? What is the range of Larkin’s cost for making lock for which the current solution will remain unchanged?
Problem 2
A large supermarket store is open from 9am to 7pm. From past experience, the supermarket knows that it needs the following number of cashiers: 9 – 10a…