From the book Managerial Uses of Accounting Information by Joel S. Demski from 2

Question

From the book Managerial Uses of Accounting Information by Joel S. Demski from 2008.

Chapter 11 q. 9

9. accounting library and decision frame Ralph's Library is a two product firm. Quantities of the two products are denoted qi and q2. Ralph has studied the situation, and decided to rely on the following LLAs DL = 90q1 + 95q2 DM = 50q1 + 100p direct labor cost direct material cost first overhead pool second overhead pool selling and adm Vi = 400.000 + 3(DL) = 200.000 + 1 (DM); S&A; = 700, 000 + 10g1 + 20g2 In addition, Ralph estimates total revenue via TR = 860q1 960g2. Ralph also faces capacity constraints. Machine hours are limited in each of two departments to a total of 6,000. (Each department has a capacity of 6,000 machine hours.) Machine hour requirements are as follows: product 1 product 2 department one department two So, for example, a unit of the first product requires one machine hour in department one and two machine hours in department two (a) Determine Ralph's optimal output and associated maximum profit.

Explanation / Answer

DECISION VARIABLES

LET THE NUMBER OF UNITS OF Q1 TO BE PRODUCED BE: Q1, AND

LET THE NUMBER OF UNITS OF Q2 TO BE PRODUCED BE Q2

BASED ON CONTRIBUTION MARGIN = TOTAL REV OF Q1 AND Q2 LESS TOTAL VARIABLE COST OF Q1 AND Q2

Ie. FOR Q1:

{860Q1 – (90 Q1 + 50Q1)} +

AND FOR Q2

{960Q2 – (95Q2 + 100q2)}

For direct materials DM=: 50q1 + 100q2

For direct labour DL= 90q1 + 95q2

1st overhead pool

OV1= 400,000 + 3DL

2ND OVERHEAD POOL

OV2 = 200,000 + 1DM

SELLING & ADMIN

S & A = 700,000 + 10Q1 + 20Q2

MAXIMIZE CONTRIBUTION MARGIN =

Z = {860Q1 – (90 Q1 + 50Q1)} +{960Q2 – (95Q2 + 100Q2)}

SUBJECT TO CONSTRAINTS

1Q1 + 2Q2 6000

2Q1+ 1Q2 6000

b)

Based on full costing:

Total cost of Product Q1

DM 50 q1

DL 90q1

and Product Q2

DM 95 q2

DL 100 q2

AND ADD ALL THE PRODUCTION OVERHEADS WHETHER FIXED OR VARIABLE

c)

opportunity cost of q2= 0

maximize Contribution

Z = {860Q1 – (90 Q1 + 50Q1)}

d)

let it be PRODUCT R

= DM 150 + DL 150

ALSO

2 MACHINE HOURS IN DEPT 1 + 2 HOURS IN DEPT 2

THUS

MAXIMIZE C

P> COSTS (= DM 150 + DL 150 + 2 MACHINE HOURS IN DEPT 1 + 2 HOURS IN DEPT 2)

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