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

1. Problem Description

(a) A manufacturing company requires 3 hours of direct labor to process every $N87.00$ worth of raw materials. If the company uses $N30,450.00$ worth of raw materials, what amount should it budget for direct labor at $N18.25$ per hour?

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

(i) the values of $x$ and $y$;

(ii) the interest paid by the second bank.

2. Solution Steps

(a)

First, we need to find out how many multiples of $N87.00$ are in $N30,450.00$.

Number of multiples $= \frac{30450}{87} = 350$.

Since each $N87.00$ requires 3 hours of direct labor, $N30,450.00$ requires $350 \times 3 = 1050$ hours of direct labor.

The cost of direct labor per hour is $N18.25$.

Total cost of direct labor $= 1050 \times 18.25 = 19162.50$.

(b)

(i) Let the amount invested in bank $M$ be $x$ and the amount invested in bank $N$ be $y$.

We are given that the total investment is $N8,000,000.00$, so:

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

The interest rate for bank $M$ is $6\%$ and for bank $N$ is $8\%$. The total interest received after 4 years is $N2,320,000.00$.

The simple interest formula is:

$Interest = Principal \times Rate \times Time$

$Interest = PRT$

Interest from bank $M = x \times 0.06 \times 4 = 0.24x$

Interest from bank $N = y \times 0.08 \times 4 = 0.32y$

Total interest $= 0.24x + 0.32y = 2,320,000$ --- (2)

From equation (1), we have $x = 8,000,000 - y$. Substitute this into equation (2):

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

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

$0.08y = 2,320,000 - 1,920,000$

$0.08y = 400,000$

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

Substitute $y = 5,000,000$ into equation (1):

$x + 5,000,000 = 8,000,000$

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

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

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

$Interest = y \times 0.08 \times 4 = 5,000,000 \times 0.08 \times 4 = 5,000,000 \times 0.32 = 1,600,000$

3. Final Answer

(a) The company should budget $N19,162.50$ for direct labor.

(b)

(i) $x = N3,000,000.00$ and $y = N5,000,000.00$

(ii) The interest paid by the second bank is $N1,600,000.00$