A sudden increase in the demand for smoke detectors has left Acme Alarms with in
ID: 3838114 • Letter: A
Question
A sudden increase in the demand for smoke detectors has left Acme Alarms with insufficient capacity to meet demand. The company has seen monthly demand from its retailers for its electronic and battery-operated detectors rise to 20,000 and 10,000, respectively, and Acme wishes to continue meeting demand. Acme’s production process involves three departments: Fabrication, Assembly, and Shipping. The relevant quantitative data on production and prices are summarized below.
Department
Monthly hours available
Hours/unit (electronic)
Hours/unit (battery)
Fabrication
2000
0.15
0.10
Assembly
4200
0.20
0.20
Shipping
2500
0.10
0.15
Variable cost/unit
$18.80
$16.00
Retail price
$29.50
$28.00
The company also has the option to obtain additional units from a subcontractor, who has offered to supply up to 20,000 units per month in any combination of electronic and battery-operated models, at a charge of $21.50 per unit. For this price, the subcontractor will test and ship its models directly to the retailers without using Acme’s production process.
1.) Acme wants an implementable schedule, so all quantities must be integers. What are the maximum profit and the corresponding make/buy levels?
2.) Compare the maximum profit in (a) to the maximum profit achievable without integer constraints. Does the integer solution correspond to the rounded-off values of the noninteger solution? By how much (in percentage terms) do the integer restrictions alter the value of the optimal objective function?
Department
Monthly hours available
Hours/unit (electronic)
Hours/unit (battery)
Fabrication
2000
0.15
0.10
Assembly
4200
0.20
0.20
Shipping
2500
0.10
0.15
Variable cost/unit
$18.80
$16.00
Retail price
$29.50
$28.00
Explanation / Answer
In the above problem one has to find optimum allocation of resources to make possible output with the available input. The unsatisfied PRODUCTION has to purchased from a sub contractor
First
The demand for Electonic devices is 20000
The demand for Battery devices is 10000
For 20000 Electronic and 10000 battery devices total availability of shipping and assembly is not enough
I.e Total Assembly time required is 20000*0.13+10000*0.12= 3800 ( But there is only 3200 hours available. so you will not able to satisfy the demand through production, remianing you have to buy from sub contractor)
Total shipping hours required is 20000*0.11+10000*0.15 = 3700 ( Total shippping hours available is 2700 only)
But for the fabrication we have enough hours . 20000*0.11 +10000*0.1 =3200 ( Only for fabrication we have more material than required)
SInce all the products required to be processed to these one must has to find optimal number of units to be produced with the help of LPP, and can solve with the help of MS EXCEL
The objective function is
Max Z= (29.70-18.20)*X1+(29.80-17.90)*x2
I.e. Max Z= 11.5X1+11.9X2
Subject to
0.11X1+0.1X2<=4400 (Fabrication Constraint)
0.13X1+0.12X2<=3200 (Assembly Constraint)
0.11X1+0.15X2<=2700 ( Shipping Constraint)
x1<= 20000,(Demand constriant for electronic)
x2<=10000 ( Demand COnstraint of Battery)
X1,X2>=0 (Non negativity constraint)
The solver Solution USING MS EXCEL or BY gRAPHICAL METHOD is as follows
The solution is to produce 20000 units of Electronic and 3333.33 units (3333 units) of battery and thus earn a Profit of 11.5*20000+11.9*3333 =$269662 from Manufaturing
But among 10000 battery required only 3333 is manufactured remaining 10000-3333= 6667 units to purchased from sub contractor at price 22.7 $ and can be sold at $ 29.80
These 6667 units has a profit margin of only 29.80-22.7 = $ 7.1 per Unit
Total profit from 6667 units = 6667*7.1=47335.7$
Total profit to the organisation
By making of 20000 electronic and 3333 units of Battery is $269662
and By purchasing and selling of 6667 units is $47335.7
Total Profit = 269662+47335.7= $316997.7
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.