# Manufacturing and Sales Decisions with Limited Resources

## 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