A company makes two products A and B, using a single resource pool. The resource is available for 900 minutes per day. The contribution margins for A and B are $20 and $35 per unit respectively. The unit loads are 10 and 20 minutes per unit.

a. Which product is more profitable?
b. The company wishes to produce a mix of 60% As and 40% Bs. What is the effective capacity (units per day)?
c. At the indicated product mix, what is the financial capacity (profit per day)?

The answers are:

a. product A is more profitable

b. Effective capacities (units per day): Product A = 54 units,  Product B = 18 units

c. the financial capacity (profit per day) = $1,710

Explanation:

a. To calculate the profit, we have to first define the term contribution margin; it refers to the net price sold on the unit of a product after variable costs have been deducted. It can be said to be the profit made on each unit of a product.

Now, we are told that Product A takes 10 minutes to produce, and its contribution margin is $20, meaning that for every 10 minutes of labor input, $20 profit is realized. the same explanation holds for product B which has a contribution margin of $35 and unit load is 20 minutes.

To get the profitable product, we will first calculate the contribution margin for 1 minute for each product;

Product A;

10 minutes = $20

∴ 1 minute = 20 ÷ 10 = $2 ( for every 1 minute of labor input $2 is made)

Product B;

20 minutes = $35

∴ 1 minute = 35 ÷ 20 = $1.75 (for every 1 minute of labor input $1.75 is made)

since more money is made o product A for every 1 minute labor input, it has more profit

b. Total minute per day = 900

Note that product A is set at 60%, meaning that out of this 900 minutes, product A will take 60%, therefore, 60% of 900 = 60/100×900

= 0.6 ×900 = 540 minutes, so product A will take up 540 minutes in a day

Product B is set at 40%, since we know that product A will take 540 out of 900 minutes, we can calculate the number of minutes for product B as;

900 - 540 =360 minutes.

Therefore product A = 540 minutes per day

product B = 360 minutes per day

Effective capacity or units produced per day is calculated thus;

Product A,

10 minutes = 1 unit (unit load, given)

∴ 540 minutes = (1 ÷ 10) × 540 = 54 units per day

Product B;

20 minutes = 1 unit

∴ 360 minutes = (1 ÷ 20 ) × 360 = 18 units per day.

c. Profits per day using number of units calculated in b above

Product A;

1 unit = $20 (given)

∴ 54 units = 20 × 54 = $1,080 profit per day

Product B;

1 unit = $35

∴ 18 units = 35 × 18 = $630 profit per day

Therefore total profit per day = $1,080 + $630 = $1,710

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