Chapter 4, Problem 71P

a.

To determine

Calculate the operating profit in case of satisfying all the annual demands.

Answer to Problem 71P

The operating profit is $672,000 in case of satisfying all the annual demands.

Explanation of Solution

Operating profit:

The operating profit is the excess of total revenues over total expenses after adjusting for depreciation and taxes.

Calculate the operating profit:

Particulars	Basic (a)	Classic (a)	Formal (a)	Total $\left(\text{d = (a + b + c)}\right)$
Total revenue (2)	$600,000	$640,000	$5,700,000	$6,940,000
Less: variable costs
Direct material (2)	$200,000	$60,000	$360,000	$620,000
Direct labor (2)	$224,000	$320,000	$3,360,000	$3,904,000
Variable overhead (2)	$56,000	$80,000	$840,000	$976,000
Variable marketing  (3)	$60,000	$64,000	$570,000	$694,000
Total variable costs	$540,000	$524,000	$5,130,000	$6,194,000
Contribution margin	$60,000	$116,000	$570,000	$746,000
Fixed cost				$74,000
Operating profit				$672,000

Table: (1)

Thus, the operating profit is $672,000 in case of satisfying all the annual demands.

Working note 1:

Calculate the revenue and costs:

Particulars	Units (a)	Rate (b)	Amount $\text{c = (a}\times \text{b)}$
Revenue:
Basic	20,000	$30	$600,000
Classic	10,000	$64	$640,000
Formal	30,000	$190	$5,700,000
Direct material:
Basic	20,000	$10	$200,000
Classic	10,000	$6	$60,000
Formal	30,000	$12	$360,000
Direct labor:
Basic	20,000	$11	$224,000
Classic	10,000	$32	$320,000
Formal	30,000	$112	$3,360,000
Variable overhead:
Basic	20,000	$3	$56,000
Classic	10,000	$8	$80,000
Formal	30,000	$28	$840,000

Table: (2)

Working note 3:

Calculate the variable marketing costs:

Particulars	Revenue (a)	Rate (b)	Amount$\text{c = (a}\times \text{b)}$
Basic	$600,000	10%	$60,000
Classic	$640,000	10%	$64,000
Formal	$5,700,000	10%	$570,000

Table: (3)

b.

To determine

Calculate the most profitable product.

Answer to Problem 71P

The most profitable product line is classic.

Explanation of Solution

Contribution margin:

The excess of sales price over the variable expenses is referred to as the contribution margin. It is computed by deducting the variable expenses from the sales revenue. A contribution margin income statement is prepared in order to record the contribution margin.

Calculate the contribution margin per constrain:

Particulars	Basic	Classic	Formal
Contribution margin	$60,000	$116,000	$570,000
Units	20000	10000	30000
Contribution margin per unit	$3	$11.9	$19
Hours per unit	0.7	2	7
Contribution margin per constrained	$4.29	$5.80	$2.71

Table: (4)

The product line with the highest contribution margin per constrained resource will be most profitable. The classic product line is the most profitable as the profit is $5.8.

Thus, the most profitable product line is classic.

c.

To determine

Recommend the product mix as per the given information.

Answer to Problem 71P

The ideal product mix should be 10,000 units of Classic and 14,285 units of Basic.

Explanation of Solution

Product mix:

When a company deals in more than one product, then it has to establish a product mix for its products. The company has limited resources, so it can only produce a limited number of products. It has to consider all the factors and recognize which product mix is most profitable for the company.

Calculate the ideal product mix:

The classic product line is the most profitable product line. It has the highest contribution margin of $5.8, so the management if the company should produce the product of classic line to its highest demand which is 10,000 units.

Company total has 30,000 hours. 10,000 units of Classic product will require 20,000$\left(\frac{10,000}{2}\right)$. So the company is left with 10,000 hours. It will produce product line Basic which has the second highest contribution margin of $4.28. The company can produce 14,285 $\left(\frac{10,000}{0.7}\right)$ units of Basic.

Thus, the ideal product mix should be 10,000 units of Classic and 14,285 units of Basic.

d.

To determine

Calculate the operating profit in case of ideal product mix.

Answer to Problem 71P

The operating profit is $84,855 in case of ideal product mix.

Explanation of Solution

Operating profit:

The operating profit is the excess of total revenues over total expenses after adjusting for depreciation and taxes.

Calculate the operating profit in case of ideal product mix:

Particulars	Basic	Classic	Total
Total revenue	$428,550	$640,000	$1,068,550
Less: variable costs
Direct material	$142,850	$60,000	$202,850
Direct labor	$159,992	$320,000	$479,992
Variable overhead	$39,998	$80,000	$119,998
Variable marketing	$42,855	$64,000	$106,855
Total variable costs	$385,695	$524,000	$909,695
Contribution margin	$42,855	$116,000	$158,855
Fixed cost			$74,000
Operating profit			$84,855

Table: (5)

Thus, the operating profit is $84,855 in case of ideal product mix.

Working note 4:

Calculate the revenue and costs:

Particulars	Units	Rate	Amount
Revenue:
Basic	14,285	$30	$428,550
Classic	10,000	$64	$640,000
Direct material:
Basic	14,285	$10	$142,850
Classic	10,000	$6	$60,000
Direct labor:
Basic	14,285	$11	$159,992
Classic	10,000	$32	$320,000
Variable overhead:
Basic	14,285	$3	$39,998
Classic	10,000	$8	$80,000

Table: (6)

Working note 5:

Calculate the variable marketing costs:

Particulars	Revenue	Rate	Amount
Basic	$428,550	10%	$42,855
Classic	$640,000	10%	$64,000

Table: (7)

e.

To determine

Calculate the additional company should produce as per the conditions.

Answer to Problem 71P

The operating profit is $5,143 in case of ideal product mix.

Explanation of Solution

Contribution margin:

Contribution margin is the amount left for the profit and fixed cost of the business. It is calculated by subtracting the variable cost from the revenue of the business.

Calculate the change in contribution margin:

Contribution margin before the increase in the labor costs is $3, $11.6 and $19 for Basic, Classic, and Formal.

Particulars	Contribution margin	Labor hours	Hour cost	Labor costs	Adjusted contribution margin
Basic	$3	0.7	$3	$2.10	$0.90
Classic	$11.6	2.0	$3	$6.00	$5.60
Formal	$19	7.0	$3	$21.00	-$2.00

Table: (8)

The contribution margin is highest in case of Classic, but it cannot produce any more units because it has already produced till the highest potential. So it has to produce the product with the second highest contribution margin which is Basic.

It is already producing 14,285 units of Basic so it can produce 5,715 $\left(20,000–14,285\right)$

The profit on one unit of Basic is $0.9, so the Company can earn $5,143$(5,715\times \text{ 0}\text{.9)}$.

Thus, the operating profit is $5,143 in case of ideal product mix.