Chapter 3.6, Problem 34PPS

(a)

To determine

To write: The total amount that has been spent on the flowers by the use of matrix multiplication.

Answer to Problem 34PPS

The total amount spent on the flowers is $\$747.50$ .

Explanation of Solution

Given information:

Students bought 200 roses, 150 daffodils and 100 orchids.

The purchase price and the sales price of the flowers is represented below in Table 1.

Flower	Purchase price	Sales Price
Rose	$1.67	$3.00
Daffodil	$1.03	$2.25
orchid	$2.59	$4.50

Calculation:

The row matrix for the number of flowers sold can be represented as,

  $A=\left[\begin{array}{ccc}200& 150& 100\end{array}\right]$

The column matrix for the purchase price of each flower can be represented as,

  $B=\left[\begin{array}{c}1.67\\ 1.03\\ 2.59\end{array}\right]$

Now multiply the two matrices $A\text{ and }B$ to obtain the total amount spent on the flowers.

The product of two matrices can be obtained by multiplying the numbers in the first row by the numbers in the first column of the matrix.

  $\begin{array}{c}AB=\left[\begin{array}{ccc}200& 150& 100\end{array}\right]\left[\begin{array}{c}1.67\\ 1.03\\ 2.59\end{array}\right]\\ =\left[200\left(1.67\right)+150\left(1.03\right)+100\left(2.59\right)\right]\\ =\left[334+154.50+259\right]\\ =\left[747.50\right]\end{array}$

Therefore, the total amount spent on the flowers is $\$747.50$ .

Conclusion:

Thus, the total amount spent on the flowers is $\$747.50$ .

(b)

To determine

To find: The total amount received on the sale of flowers by the use of multiplication.

Answer to Problem 34PPS

The total amount received on the sale of flowers is $\$1387.50$ .

Explanation of Solution

Given information:

Students bought 200 roses, 150 daffodils and 100 orchids.

The purchase price and the sales price of the flowers is represented below in Table 1.

Flower	Purchase price	Sales Price
Rose	$1.67	$3.00
Daffodil	$1.03	$2.25
orchid	$2.59	$4.50

Calculation:

The row matrix for the number of flowers sold can be represented as,

  $A=\left[\begin{array}{ccc}200& 150& 100\end{array}\right]$

The column matrix for the sales price of each flower can be represented as,

  $C=\left[\begin{array}{c}3.00\\ 2.25\\ 4.50\end{array}\right]$

Now multiply the two matrices $A\text{ and }C$ to obtain the total amount received on the flowers.

  $\begin{array}{c}AC=\left[\begin{array}{ccc}200& 150& 100\end{array}\right]\left[\begin{array}{c}3.00\\ 2.25\\ 4.50\end{array}\right]\\ =\left[200\left(3.00\right)+150\left(2.25\right)+100\left(4.50\right)\right]\\ =\left[600+337.5+450\right]\\ =\left[1387.5\right]\end{array}$

Therefore, the total amount received on the flowers is $\$1387.50$ .

Conclusion:

Thus, the total amount received on the flowers is $\$1387.50$ .

(c)

To determine

To find: The amount of the profit made by the students on the sale of the flowers.

Answer to Problem 34PPS

The profitable amount is $\$650$ on the sale of the flowers.

Explanation of Solution

Calculation:

Profit is the valuable return in which revenue exceeds the cost of the product.

The purchase price matrix is $\left[747.5\right]$ and the sales price matrix is $1387.5$ .

Subtract the purchase price from the sales matrix to obtain the profit made by the students on the sales of the flower.

  $\begin{array}{c}\text{profit}=\left[1387.5\right]-\left[747.5\right]\\ =\left[640\right]\end{array}$

Therefore, the profitable amount is $\$650$ on the sale of the flowers.

Conclusion:

Thus, the profitable amount is $\$650$ on the sale of the flowers.