2- I want solution of this question with all steps, please. ThanksBig Thumb October sales at the Market in shop1 and shop 2 are given in the following table.shop1Shop2Blades4030Fluid(bottles)2024mats168The usual selling prices for these items are OMR 6 each for blades,OMR 3 per bottlefor fluid, and OMR 12 each for mats. The discount prices for A- plus club membersare OMR 6 each for blades, OMR 2 per bottle for fluid, and OMR 10 each for floormats. Use matrix multiplication to compute the total revenue at each shop, assumingfirst that all items were sold at the usual prices, and then that they were all sold atthe discount prices.2.

Answered: October sales at the Market in shop1…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2- I want solution of this question with all steps, please. Thanks

Big Thumb

October sales at the Market in shop1 and shop 2 are given in the following table.
shop1
Shop2
Blades
40
30
Fluid(bottles)
20
24
mats
16
8
The usual selling prices for these items are OMR 6 each for blades,OMR 3 per bottle
for fluid, and OMR 12 each for mats. The discount prices for A- plus club members
are OMR 6 each for blades, OMR 2 per bottle for fluid, and OMR 10 each for floor
mats. Use matrix multiplication to compute the total revenue at each shop, assuming
first that all items were sold at the usual prices, and then that they were all sold at
the discount prices.
2.

Expert Solution

Step 1

Given:

The usual selling price per blade is OMR 6.

The usual selling price per bottle of fluid is OMR 3.

The usual selling price per mat is OMR 12.

These selling prices can be assigned by column vector $S = [\begin{matrix} 6 \\ 3 \\ 12 \end{matrix}]$ .

The discount selling price per blade is OMR 6.

The discount selling price per bottle of fluid is OMR 2.

The discount selling price per mat is OMR 10.

These discount prices can be assigned by column vector $D = [\begin{matrix} 6 \\ 2 \\ 10 \end{matrix}]$ .

From the given table of October sales of shop 1 and shop 2 it can be seen that:

Shop 1 sells 40 blades, 20 bottles of fluid and 16 mats.

The number of items sold can be assigned row vector $P_{1} = [\begin{matrix} 40 & 20 & 16 \end{matrix}]$ .

Shop 2 sells 30 blades, 24 bottles of fluid and 8 mats.

The number of items sold can be assigned row vector $P_{2} = [\begin{matrix} 30 & 24 & 8 \end{matrix}]$ .

Step 2

Total revenue of shop 1 when items are sold at usual price is given by matrix multiplication P₁S as below:

$P_{1} S = [\begin{matrix} 40 & 20 & 16 \end{matrix}] [\begin{matrix} 6 \\ 3 \\ 12 \end{matrix}] = [40 \times 6 + 20 \times 3 + 16 \times 12] = [240 + 60 + 192] = 492$

Therefore, the revenue of shop 1 when items are sold at usual price is OMR 492.

Total revenue of shop 1 when items are sold at discount price is given by matrix multiplication P₁D as below:

$P_{1} D = [\begin{matrix} 40 & 20 & 16 \end{matrix}] [\begin{matrix} 6 \\ 2 \\ 10 \end{matrix}] = [40 \times 6 + 20 \times 2 + 16 \times 10] = [240 + 40 + 160] = 440$

Therefore, the revenue of shop 1 when items are sold at discount price is OMR 440.

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