Question

a florist makes three special flower arrangements. one uses three lilies. the second uses five lilies and two carnations. the third uses five daisies and two carnations. lilies cost $2.25 each, carnations cost $0.90 each, and daisies cost $1.20 each. complete parts (a) through (c) below.
arrangement 3 0 2 5
(b) write a matrix to show the cost of each type of flower.
2.25
0.90 (type integers or decimals.)
1.20
(c) find the matrix showing the cost of each floral arrangement.
□
□ (type integers or decimals. simplify your answers.)
□

Explanation:

Step1: Let matrix \(A\) be the number of flowers in each arrangement

Arrangement 1: \([3\quad0\quad0]\) (3 lilies, 0 carnations, 0 daisies)
Arrangement 2: \([5\quad2\quad0]\) (5 lilies, 2 carnations, 0 daisies)
Arrangement 3: \([0\quad2\quad5]\) (0 lilies, 2 carnations, 5 daisies)
So, \(A=

$$\begin{bmatrix}3&0&0\\5&2&0\\0&2&5\end{bmatrix}$$

\)

Step2: Let matrix \(B\) be the cost of each type of flower

\(B =

$$\begin{bmatrix}2.25\\0.90\\1.20\end{bmatrix}$$

\)

Step3: Calculate the cost of each arrangement using matrix multiplication \(C = A\times B\)

For Arrangement 1: \(3\times2.25+0\times0.90 + 0\times1.20=6.75\)
For Arrangement 2: \(5\times2.25+2\times0.90+0\times1.20 = 11.25 + 1.80=13.05\)
For Arrangement 3: \(0\times2.25+2\times0.90+5\times1.20=1.80 + 6.00 = 7.80\)

Answer:

\(

$$\begin{bmatrix}6.75\\13.05\\7.80\end{bmatrix}$$

\)