To find the total number of units of raw material used to produce the 2,000 park benches, let's work through the problem step-by-step.

Step 1: Calculate the standard quantity of raw material required

Each park bench requires 3 feet of raw material.

$\text{Standard quantity required} = 2{,}000 \text{ benches} \times 3 \text{ feet/bench} = 6{,}000 \text{ feet}$

Step 2: Account for the direct materials quantity variance

The problem states there was an unfavorable direct materials quantity variance of $6,000. This implies that more material was used than the standard amount, leading to an excess cost.

To calculate how much more material was used, we need to find the cost per unit of raw material under the standard cost:

1. Standard cost of material = $100,000 for 6,000 feet (standard usage for 2,000 benches).
2. Cost per foot = $\frac{100{,}000}{6{,}000} = 16.67$ dollars per foot.

Step 3: Determine excess material used due to variance

Using the cost per foot, we can calculate the excess material used:

$\text{Excess material cost} = 6{,}000 \, \text{dollars}$ $\text{Excess material quantity} = \frac{6{,}000}{16.67} \approx 360 \text{ feet}$

Step 4: Calculate the total material used

$\text{Total material used} = \text{Standard quantity} + \text{Excess quantity} = 6{,}000 + 360 = 6{,}360 \text{ feet}$

Final Answer

The total amount of raw material used to produce the 2,000 park benches was 6,360 feet.

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Related Questions

1. How would a favorable variance affect the total material used?
2. How can the cost per foot of material impact the variance?
3. What if the standard cost for material output changed to $90,000?
4. How would a change in the number of park benches produced affect the standard material requirement?
5. What impact would switching to a more efficient material have on future variance?

Tip: Variance analysis can help identify areas for operational efficiency improvements by tracking differences between actual and standard costs.