Question

Which retailer should each dealer choose for its purchase? Use matrix multiplication.

Answer 1

Given:

Bill's wants to buy 360 small jerseys, 540 medium jerseys, and 300 large jerseys.

Bud's wants to buy 240 small jerseys, 600 medium jerseys, and 360 large jerseys.

Zest charges $14 for small jerseys, $ 18 for medium jerseys, and $ 21 for large jerseys.

Zeal charges $16 for small jerseys, $ 18 for medium jerseys, and $ 19 for large jerseys.

Required:

We need to find dealers that each retailer chooses to purchase

Step-by-step explanation:

The matrix for the given model is

`Matric\text{ for purchase =}\begin{bmatrix}{360} & {540} & {300} \\ {} & {} & \text{ }{} \\ {240} & {600} & {360}\end{bmatrix}`

The first row represents Bill's purchase.

The second row represents Bud's purchase.

`Matric\text{ for dealers price =}\begin{bmatrix}{14} & {} & {16} \\ {18} & {} & {18} \\ {21} & {} & {19}\end{bmatrix}`

The first column represents Zest price.

The second column represents Zeal price

Multiply both matrices.

`=\begin{bmatrix}{{(360*14)}+(540*18)+(300*21)} & {{{(360*16)}+(540*18)+(300*19)}} \\ {(240*14)}+(600*18)+(360*21) & {{(240*16)}+(600*18)+(360*19)}\end{bmatrix}`
`=\begin{bmatrix}21060 & 21180 \\ 21720 & 21480\end{bmatrix}`

The first row is for Bill.

The minimum value is 21060.

Bill should choose Zest.

The second row is for BUd.

The minimum value is 21480.

Bud should choose Zeal.

Final answer:

Bill should purchase from Zest, Bud should purchase from Zeal.