Manufacturing and Sales Decisions with Limited Resources

Posted on Aug 22, 2024 in Mathematics

HO # 7 – Manufacturing of Two Products with Limited Resources

Objective

(1) Objective Criterion: Maximize profit subject to constraining factors.

(2) Find the binding constraint (technological) given the market/demand constraint.

Resource Availability and Requirements

Hours Available:

DLHRS: 10,000
MHRS: 14,000

Hours Required to Produce:

24,000 units of Product A: 8,000 DLHRS, 12,000 MHRS
6,000 units of Product B: 6,000 DLHRS, 2,000 MHRS

Total Hours Required for 24,000 A & 6,000 B:

DLHRS: 14,000
MHRS: 14,000

Contribution Margin (CM) per Unit:

Product A: $3
Product B: $6

Units per DLHR:

Product A: March 1
Product B: 1

CM per DLHR:

Product A: $9
Product B: $6

Ranking in Order of Profitability:

Product A: 1st
Product B: 2nd

Government Contract vs. Regular Channels

Government Contract	Regular Channels	Total
As above: In neither of $3,500	5,000 sales x $6	$30,000
	Less Expenses
	Mfg 5,000 x $3 = $15,000
	Selling 5,000 x $1.50 = $7,500	$22,500
	(FC Irrelevant)
	In neither	$7,500

Avoidable Costs

There are two products, and enough MHRS for all the units of A & B that can be sold. But there are not enough DLHRS.

Therefore, DLHRS is the binding (scarce) constraint.

Determining CM per DLHR and Ranking Profitability

(3) Determine the CM per DLHR for each product (A & B) and then rank in order of profitability.

HO # 9

Objective Function = OR_n + OR_o >= $50,000

OR_n = TCM_n – FC_n

Let X_n = D_n = units of product produced & sold new.

F_or = FOHB / D_or

Therefore, FOHB = F_or x D_or = $0.50 x 240,000 units = $120,000

F_n = FOHB / D_n

D_n = FOHB / F_n = $120,000 / $1 = 120,000 units

Expected units of production & sales of the new product must be half of old production: (1/2 x 240,000) = 120,000 units

Factory FOH rate is twice that of the old product.

Therefore, OR_n = TCM_n – FC_n = (X_n x CM/U_n) – X_n(F_n + F_s&a/U_n) = (120,000 x $2) – 120,000($1 + $0.50) = $240,000 – 120,000 x $1.50 = $240,000 – $180,000 = $60,000

But NOR_n + OR_o = $50,000/yr.

DNI_or = $(50,000 – $60,000) = $10,000 loss

X_or = (FC + DNI_or) / CM/unit = (F_s&a + DNI) / (SP/U – V_s&a – P)

240,000 = ((240,000 x $0.90) – $10,000) / ($6 – $1.20 – P) = ($216,000 – $10,000) / ($4.80 – P) = $1,152,000 – $240,000P = $206,000

P = $3.94167

This is an example of opportunity cost whereby subcontracting at a price well above $3.50 (the full unit manufacturing cost) is still desirable because the old product will be displaced in manufacturing a new product which is more profitable.

HO # 8 – Pen Manufacturer

Denominator Current Level (D) = 20,000 units/month or 240,000 units/year

FOHR = FOHB / D

$0.50 = FOHB / 240,000

FOHB = $120,000 per year

Question 1

(B) $(1.00 + $1.20 + $0.80 + $0.50) = $3.50 (Conventional/Absorption/Full Costing)

Question 2

(E) Note – Irrelevant Fixed Costs

Original SP: $6.00

Variable Expenses: $4.50

Original CM/unit: $1.50

Original Total CM = $1.50 x 240,000 = $360,000/yr.

New SP: $5.80

Variable Expenses: $4.50

New CM/unit: $1.30

Total New CM = $1.30 x 264,000 = $343,200/yr.

Decrease in OR = $16,800/yr.

Question 3

$3,500 – This is the one that deals with the government contract.

FOH Monthly Budget (Current) = 20,000 x $0.50 = $10,000

Applied FOH = 15,000 x $0.50 = $7,500

Under Applied FOH (Opportunity Cost Avoided) = $2,500

Fixed Fee Plus = $1,000

Total = $3,500

Were it not for the order, if landed, FOH would be under applied by $2,500. Therefore, order taking increases profit by $1,000 plus $2,500 => $3,500

Alternative Solution

Increased sales will be by 5,000 x $3.50 = $17,500 + $1,000 = $18,500

VC Mfg will be increased by 5,000 x $3.00 = $15,000 (Selling V = 0)

Increase in CM = $3,500

Change in FC (Irrelevant) = 0

Therefore, increase in profit = $3,500

Note: Assumes selling expenses are not influenced by this contract cost solution.

Question 4

(a) Decrease $4,000 ($7,500 – $3,500)

Therefore, the government contract will decrease profit from the regular channel by $4,000 ($7,500 – $3,500).

Question 5

(b) Original VC/unit = $3.00

Shipping Cost/unit = $0.75

New VC/unit = $3.75

BE_units = FC / CM/unit

10,000 = $4,000 / (P – $3.75)

10,000P – $37,500 = $4,000

P = $4.15

Question 6

$1.50 Variable Selling Expenses (What about Variable Mfg Cost? Answer – They are irrelevant because units have already been produced).

Question 7

(e) Short-cut Solution: Make and Ship High-Style Pens and Plant Becomes Idle

The highest price to be paid would be measured by the avoidable costs of halting production and subcontracting.

Variable Mfg Cost/unit: $3.00

Fixed Mfg Cost Saved: $60,000 / 240,000 = $0.25

Selling V (0.20 x $1.50) = $0.30

Total = $3.55