Lee Corporation manufactures and sells party items. The following representative direct labour hours and production costs are provided for a four-month period:
$\begin{array}{ccc}
\text { Month } & \text { Direct Labour Hours } & \text { Production } \
\hline \text { January } & 3,600 & \$ 15,000 \
\text { February } & 4,800 & 17,500 \
\text { March } & 6,000 & 20,000 \
\text { April } & 4,800 & 17,500 \
\text { Total } & 19.200 & \$ 70.000 \

\end{array}$ Let $\quad $ a = Fixed production costs per month
$\quad $ $\quad $b = Variable production costs per direct labour hour
$\quad $ $\quad $n = Number of months
$\quad $ $\quad $X = Direct labour hours per month
$\quad $ $\quad $Y = Total monthly production costs
$\quad $ $\quad $s = Summation
-Refer to the figure.What would the cost be for 5,000 labour hours?

Question

Lee Corporation manufactures and sells party items. The following representative direct labour hours and production costs are provided for a four-month period:
$\begin{array}{ccc}
 \text { Month } & \text { Direct Labour Hours } & \text { Production } \
\hline \text { January } & 3,600 & \$ 15,000 \
 \text { February } & 4,800 & 17,500 \
 \text { March } & 6,000 & 20,000 \
 \text { April } & 4,800 & 17,500 \
\text { Total } & 19.200 & \$ 70.000 \

\end{array}$ Let $\quad $ a = Fixed production costs per month
 $\quad $ $\quad $b  = Variable production costs per direct labour hour
 $\quad $ $\quad $n = Number of months
 $\quad $ $\quad $X = Direct labour hours per month
 $\quad $ $\quad $Y = Total monthly production costs
 $\quad $ $\quad $s  = Summation
-Refer to the figure.What would the cost be for 5,000 labour hours?

Quizplus · Accepted Answer

The cost for 5,000 labor hours can be determined by first finding the variable cost per labor hour and the fixed cost per month. The variable cost per labor hour (b) can be calculated by using the given data to form a linear equation based on the formula Y = a + bX, where Y is the total monthly production cost, a is the fixed production cost per month, and X is the direct labor hours per month.From the given data:- For January, with 3,600 hours, the cost is $15,000.- For February and April, with 4,800 hours, the cost is $17,500.- For March, with 6,000 hours, the cost is $20,000.Using any two points to form a linear equation, we can solve for b (variable cost per labor hour) and a (fixed cost per month). For simplicity, let's use January and March:1. $15,000 = a + b(3,600)$2. $20,000 = a + b(6,000)$Subtracting the first equation from the second gives:$5,000 = b(2,400)$Solving for b gives:$b = 5,000 / 2,400 = 2.083$Now, using b to solve for a using one of the original equations:$15,000 = a + 2.083(3,600)$$a = 15,000 - 7,500 = 7,500$Now, to find the cost for 5,000 labor hours:$Y = 7,500 + 2.083(5,000)$$Y = 7,500 + 10,415 = 17,915$Rounding to the nearest hundred gives $17,900, which is closest to option C.

Lee Corporation Manufactures and Sells Party Items Let \quad A = Fixed Production Costs Per Month

Lee Corporation Manufactures and Sells Party Items Let $\quad$ A = Fixed Production Costs Per Month