The problem consists of two parts: (a) A manufacturing company uses 3 hours of direct labor to process N87.00 worth of raw materials. The company uses N30,450.00 worth of raw materials. We need to find the amount to budget for direct labor at N18.25 per hour. (b) An investor invested Nx in bank M at 6% simple interest per annum and Ny in bank N at 8% simple interest per annum. A total of N8,000,000.00 was invested in the two banks, and the investor received N2,320,000.00 as interest after 4 years. We need to calculate: (i) the values of x and y; (ii) the interest paid by the second bank.

1. Problem Description

The problem consists of two parts:

(a) A manufacturing company uses 3 hours of direct labor to process N87.00 worth of raw materials. The company uses N30,450.00 worth of raw materials. We need to find the amount to budget for direct labor at N18.25 per hour.

(b) An investor invested Nx in bank M at 6% simple interest per annum and Ny in bank N at 8% simple interest per annum. A total of N8,000,000.00 was invested in the two banks, and the investor received N2,320,000.00 as interest after 4 years. We need to calculate:

(i) the values of x and y;

(ii) the interest paid by the second bank.

2. Solution Steps

(a)

First, we calculate how many sets of N87.00 are in N30,450.

0

0. $Sets = \frac{30450}{87} = 350$

Each set requires 3 hours of direct labor, so the total labor hours are:

$TotalHours = 350 \times 3 = 1050$

The cost per hour is N18.25, so the total cost is:

$TotalCost = 1050 \times 18.25 = 19162.5$

(b)

(i) We know that the total investment is N8,000,000.

0

0. Therefore:

$x + y = 8,000,000$ (Equation 1)

The total interest received after 4 years is N2,320,000.

0

0. The simple interest formula is:

$Interest = Principal \times Rate \times Time$

$I = PRT$

The interest from bank M is $0.06 \times x \times 4 = 0.24x$

The interest from bank N is $0.08 \times y \times 4 = 0.32y$

The total interest is $0.24x + 0.32y = 2,320,000$ (Equation 2)

We can solve this system of equations. First, solve Equation 1 for x:

$x = 8,000,000 - y$

Substitute this into Equation 2:

$0.24(8,000,000 - y) + 0.32y = 2,320,000$

$1,920,000 - 0.24y + 0.32y = 2,320,000$

$0.08y = 400,000$

$y = \frac{400,000}{0.08} = 5,000,000$

Now, substitute y back into Equation 1 to find x:

$x = 8,000,000 - 5,000,000 = 3,000,000$

So, $x = 3,000,000$ and $y = 5,000,000$.

(ii)

The interest paid by the second bank (bank N) is:

$Interest_N = 0.08 \times y \times 4 = 0.08 \times 5,000,000 \times 4 = 1,600,000$

3. Final Answer

(a) The amount to budget for direct labor is N19,162.

5

0. (b)

(i) $x = 3,000,000$ and $y = 5,000,000$.

(ii) The interest paid by the second bank is N1,600,000.

0

0.