Question

1.     The annual sale volumes of three products  X, Y, Z whose sale prices per unit are GHS 3.50, GHS 2.75, GHS 1.50 respectively, in two different markets I and II are shown below:                                                      Product                  Market               X             Y              Z                     I                     6000      9000         1300                    II                    12000    6000          17000             Find the total revenue in each market with the help of matrices.​

Answer 1

Explanation:

To find the total revenue in each market, we can calculate the product of the sale volumes and sale prices per unit using matrices.

Let's represent the sale volumes as a matrix V and the sale prices per unit as a matrix P:

V = [6000 9000 1300]

[12000 6000 17000]

P = [3.50]

[2.75]

[1.50]

To calculate the total revenue in each market, we need to perform matrix multiplication between V and P, considering the appropriate dimensions. The resulting matrix will give us the total revenue for each product in each market.

Total revenue = V * P

Calculating the matrix multiplication:

[6000 9000 1300] [3.50] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[12000 6000 17000] [2.75] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

Performing the calculation:

[60003.50 + 90002.75 + 13001.50] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[120003.50 + 60002.75 + 170001.50] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

Simplifying the calculation:

[21000 + 24750 + 1950] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[42000 + 16500 + 25500] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

[47650] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]

[84000] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]

Therefore, the total revenue in Market I is GHS 47,650 and the total revenue in Market II is GHS 84,000.