Let's analyze each statement one by one.
-
Given the manufacturing cost per kite, it is possible that Kate’s Kites manufactures 600 kites at a total manufacturing cost of $522.
- To find the total cost of 600 kites at $1.07 each: \[ 600 \text{ kites} \times 1.07 \text{ dollars/kite} = 642 \text{ dollars} \]
- The statement that the total manufacturing cost is $522 is not possible, as it is lower than the calculated cost of $642.
-
From a profit maximization standpoint, it would be preferable to produce kites at a manufacturing cost of $1.09 per kite.
- Higher manufacturing costs without additional value generally decrease profit margins. Therefore, this statement is not true since profit maximization typically requires lower manufacturing costs.
-
If Kate’s Kites could hire additional staff and produce 800 kites at a total cost of $947, this will reduce the average manufacturing cost per kite.
- First, calculate the average cost per kite for 800 kites at $947: \[ \text{Average cost} = \frac{947 \text{ dollars}}{800 \text{ kites}} = 1.18375 \text{ dollars/kite} \]
- Since this average cost ($1.18375) is greater than the current manufacturing cost of $1.07 per kite, this statement is not true.
-
If Kate’s Kites could hire additional staff and produce 800 kites at a manufacturing cost of $816, this will reduce the average manufacturing cost per kite.
- Calculate the average cost per kite for 800 kites at $816: \[ \text{Average cost} = \frac{816 \text{ dollars}}{800 \text{ kites}} = 1.02 \text{ dollars/kite} \]
- This average cost ($1.02) is lower than the current manufacturing cost of $1.07 per kite, which means this statement is true.
In summary, the true statement is:
If Kate’s Kites could hire additional staff and produce 800 kites at a manufacturing cost of $816, this will reduce the average manufacturing cost per kite.
1 answer