Question

LP Large Problem (4 marks for question, 6 marks for worksheet) A company sells three products: A, B, and C. The company has customer orders for 2,000 units of A, 3.750 B's, and 1,700 C's. The company makes the products in-house, which requires production and shipping resources (constraints 1, 2) as shown in the table below. The company can outsource some demand for A and B, but cannot outsource C. Outsourcing requires no production or shipping resources. The company wants to make at least 3,000 units in-house (constraint 3), satisfy as many orders as possible (constraints 4, 5, 6), and maximize total profit (objective function (). Product Selling price $20 $25 $30 A Decision variables Make (M) Outsource (S) AM AS BM BS CM Cost per product Make Outsource $13 $16 $16 $20 $18 Available hours Resources to make (M) product Production Shipping 4 hours 1 hour 5 B 16,500 hours 6,500 hours

Answer 1

option 1

Cost with constraint 1 (i.e. production)
	A	B	C
SP	$20	$25	$30
Cost	$13	$16	$16
contribution	$7	$9	$14
no. of hours	4	5	6
total contribution /hour	1.75	1.8	2.333333
rank	3rd	2nd	1st
advice	outsource	balance inhouse	inhouse
Allocation of units for inhouse /outsourcing
product	no. of units	hours required p.u	total hours
C	1700	6	10200
B	1260	5	6300
	(in house)
B	2490
	(outsourcing)
A	2000(outsourcing)
total hours available	2960		16500
Profit statement
particulars	A	B	C	total
Order units	2000	3750	1700	7450
SP	$20	$25	$30	75
Total Sales	$40,000	$93,750	$51,000	184750
Cost
in house		$20,160	$30,600	$50,760
		(1260*16)	(1700*18)
outsourcing	$32,000	$49,800		81800
	(2000*16)	(2490*20)
total	32000	69960	30600	132560
Profit	$8,000	$23,790	$20,400	$52,190

Therefore profit under constraint 1 (production )is $ 52190

option 2

Cost with constraint 2 (i.e. shipping resources)
	A	B	C
SP	$20	$25	$30
Cost	$13	$16	$16
contribution(A)	$7	$9	$14
no. of hours(B)	1	2	2
total contribution /hour(A/B)	7	4.5	7
rank	2nd	3rd	1st
advice	inhouse	outsource	inhouse
Allocation of units for inhouse /outsourcing
product	no. of units	hours required p.u	total hours
C	1700	2	3400
A	775	4	3100
	(in house)
A	1225
	(outsourcing)
B	3750(outsourcing)
total hours available			6500
Profit statement
particulars	A	B	C	total
Order units	2000	3750	1700	7450
SP	$20	$25	$30	75
Total Sales	$40,000	$93,750	$51,000	184750
Cost
in house	10075	$75,000	$22,100	$50,760
	(775*13)	(3750*20)	(1700*18)
outsourcing	$19,600			19600
	(1225*16)
total	$29,675	$75,000	$22,100	126775
Profit	$10,325	$18,750	$28,900	$57,975

Therefore profit under constraint 2 (shipping )is $ 57975

Therefor ein order to maximise the profit, option 2 should be selected