Question

IM1	IM2	IM3	IM4	IM5
C1	3	1	0	1	2
C2	0	0	3	6	8
C3	2	3	2	3	2
Sell Price
$          235.80
$     1,325.69
$          814.28
	IM1	IM2	IM3	IM4	IM5
Available Quantities	460	300	100	450	950
Cost per 1 of Each	$                   3.38	$               30.48	$                35.86	$                   140.00	$                         3.00

1. The data provides the description for three items (C1, C2, and C3) produced by a company and the selling price of each of these items. A combination of 5 input materials (IM) are required to produce each item. The quantity of each material required to produce one unit of an item is shown, along with the cost of each input material, and the quantity of each of the input material available. Based on this information, answer the following questions:

1. What is the per unit profit margin for products C1, C2, and C3?

3. If the company were required to produce at least 15 units of C1, 28 units of C2 and 5 units of C3:

1. What would be their total profit?

2. How much quantity of the input materials are consumed?

3. Identify the input materials that are constraining the ability of the company to increase their profit.

4. List the input materials below

4. The company would like to know the most they should pay to an outside vendor for each additional input material identified in part b. iii. (Keep all constraints added in part b.) Complete the table below:

Answer 1

	C1	C2	C3	Total qty	constraint	cost	Total SP and cost
No. to be made	1	1	1	3	x	x	x
Selling price SP/unit	235	1325	814	X	X	x	x
Seling revenue	235	1325	814	X	x	x	2374
Raw materials
IM1 (3,0,2)	3	0	2	5	460	3.38	16.9
IM2(1,0,3)	1	0	3	4	300	30.48	121.92
IM3(0,3,2)	0	3	2	5	100	35.86	179.3
IM 4 (1,6,3)	1	6	3	10	450	140.00	1400
IM5 (2,8,2)	2	8	2	12	950	3.00	36
COST OF raw mat.	186.62	971.58	595.92
Unit profit margin -(SP-cost of raw material)	48.38	353.42	218.08

(a)

Product	C1	C2	C3
Unit profit margin IN $	43.38	353.42	218.08

(b) To manufacture 15 units of C1, 28 units of C2 and 5 units of C3, substututing the figures in the excel sheet;

Description	C1	C2	C3	Total qty	constraint qty	cost	Total SP , cost & profit margin
No. to be made	15	28	5	48	x	x	x
Selling price SP/unit	235	1325	814	X	X	x	x
Seling revenue(SR)	3525	37100	4070	X	x	x	44695
Raw materials
IM1 (3,0,2)	45	0	10	55	460	3.38	185.9
IM2(1,0,3)	15	0	15	30	300	30.48	914.4
IM3(0,3,2)	0	84	10	94	100	35.86	3370.84
IM 4 (1,6,3)	15	168	15	198	450	140.00	27720
IM5 (2,8,2)	30	224	10	264	950	3.00	792
COST OF raw mat.	2799.3	27204.24	2979.6				32983.14
Unit profit margin -(SP-cost of raw material)	48.38	353.42	218.08
Total profit margin=SR-Cost of raw materials	725.7	9895.76	1090.4				11711.86

(b)

i) Total profit for te above quantities to be manufactured=$11,711.86.

ii) Quantities of raw materials required are shown again in the table below:

RM qty's required for 15, 28 and 5 units respectively of C1, C2, C3
Raw material	Quantity
IM1	55
IM2	30
IM3	94
IM4	198
IM5	264

iii) It can be seen that unit profit margin per unit is in order of C2( 353.42), C3 ( 218.08) and C1 ( 48.38).

Raw material IM3 requirement of 94 is the neares to its constraint quantity of 100.

Therefore this can at best allow an increase of prod of C! which has the lowest unit margin. No further units of C2 and C3 (high unit profit margin products)can be manufactured.

Let us increase prod of C1 to increase profit (this is the only possibility in the present constraints)

LET US CALCULATE -how many units of C1 can be manufactured till constraint of each raw material is reached.

RM	reqd/unit of C1	Constraint qty	already used up	No. units of C1 possible
IM1	3	460	55	135
IM2	1	300	30	270
IM3	0	100	94	XX
IM4	1	450	198	252
IM5	2	950	264	343

Note =No. of units of CI posible for each RM. =(costraint qty-already used up qty)/RM required per unit of C1

The minimum of the above is 135 units which limits the next constraint of IM1

If we continue further (assumuing that this contraint is taken care of) , the constraints in order would be ;

IM4, IM2, IM5.

The complete hierarchy is

IM3,

IM1

IM4,

IM2,

IM5.

(c)

RM IM3 which can be bought at 353/3 ,218/2=118, 109 The higher profit being 118, so the company can be-willing to pay 118-expenses for IM3. next IM1, the ratio of additional profits here is from C1 and C3 @ 48.38/3; 218.08/2=16, 109 per unit of the RM. So payment can be 109-expenses for IM1.

Next for IM4 C3 will yield additional profit of $ 93 /unit of RM so the payment =93_expenses. IM2 would yield an additional profit of 72 for C3 Hence this can be paid upto 72-expenses. IM2--106 per unit of RM for C3 .

Now IM5 an additional profit of 109 per unit of RM for C3. so can pay 109-expenses. Summary:IM3 --109, IM 1 --109, IM4 -93, IM2-106 IM5-109.