MHB Ice cream & yogurt matrices problem

[mathlearn]

The price of a tub of ice cream and a tub of yoghurt respectively at store A and store B are given below.
Store A ( 40 , 30)
Store B ( 38 , 35)

(i) Represent the above information in a matrix of order 2 * 2, such that the columns denote the stores.

(ii) 20 tubs of ice cream and 30 tubs of yoghurt are required for a certain function. Represent these amounts by a matrix of order 1 * 2 and obtain the product of the two matrices.

(iii) By considering this product, write down with reasons, the store from which it is more advantageous to buy 20 tubs of ice cream and 30 tubs of yogurt.

So Depicting them in column matrices

i.$A=\begin{bmatrix}
40&30\\
38&35\end{bmatrix}$

ii.$B=\begin{bmatrix}
20&30\\
\end{bmatrix}$

Help me to do III and tell me whether the rest is correctly done?

 

[Joppy]

The price of a tub of ice cream and a tub of yoghurt respectively at store A and store B are given below.
Store A ( 40 , 30)
Store B ( 38 , 35)

(i) Represent the above information in a matrix of order 2 * 2, such that the columns denote the stores.

(ii) 20 tubs of ice cream and 30 tubs of yoghurt are required for a certain function. Represent these amounts by a matrix of order 1 * 2 and obtain the product of the two matrices.

(iii) By considering this product, write down with reasons, the store from which it is more advantageous to buy 20 tubs of ice cream and 30 tubs of yogurt.

So Depicting them in column matrices

i.$A=\begin{bmatrix}
40&30\\
38&35\end{bmatrix}$

ii.$B=\begin{bmatrix}
20&30\\
\end{bmatrix}$

Help me to do III and tell me whether the rest is correctly done?

I think i. should be,

$A=\begin{bmatrix}
40&38\\
30&35\end{bmatrix}$

In this way, column 1 represents store A, which stocks yogurt and ice cream at 40 and 30 units respectively. And likewise for column 2...

Btw i can't reply to your PM because your inbox is full!

 

[mathlearn]

I think i. should be,

$A=\begin{bmatrix}
40&38\\
30&35\end{bmatrix}$

In this way, column 1 represents store A, which stocks yogurt and ice cream at 40 and 30 units respectively. And likewise for column 2...

Yes I think you're very correct :) & I need help for Question II & III .

(ii) 20 tubs of ice cream and 30 tubs of yoghurt are required for a certain function. Represent these amounts by a matrix of order 1 * 2 and obtain the product of the two matrices.

(iii) By considering this product, write down with reasons, the store from which it is more advantageous to buy 20 tubs of ice cream and 30 tubs of yogurt.

Btw i can't reply to your PM because your inbox is full!

:) I think you should consider exporting the messages and deleting a folder

Many Thanks :)

 

[Joppy]

Let's answer ii. and iii. at the same time. The function requires 30 tubs of yogurt and 20 tubs of ice cream (yum..). We know what the prices for these products are at both shops A and B.

I encourage you to think about how you would solve this problem without the use of matrices as it may come more natural.

$ \begin{bmatrix} 20&30\ \end{bmatrix} * \begin{bmatrix}
40&38\\
30&35\end{bmatrix} = \begin{bmatrix}
(20*40 + 30 * 30)&(20 * 38 + 30 * 35)\\
\end{bmatrix} = \begin{bmatrix} 1700&1810\ \end{bmatrix}$

Do you know why we can multiply these two matrices together? Can you think of a case when we could not?

This settles part ii. i think, and for iii., we can easily see that the more 'advantageous' supermarket to shop from (for this order) would be shop A. This is because 1700 < 1810, where 1700 units is the price it would cost for 20 ice creams and 30 yogurts at shop A.

Hope this helps! If something doesn't make sense or i made a mistake, let me know :).

 

[mathlearn]

You're explained it perfectly :), I think you deserve an ice cream or a yogurt

View attachment 5908

Thank you very much :) Joppy

 

[Joppy]

:) I think you should consider exporting the messages and deleting a folder

Many Thanks :)

Hahaha what! It's your inbox that needs emptying!