Suppose a firm produces three types of output using two types of inputs. Its output quantities are given by column vector and the unit price of these outputs are given by row vector . The amount of inputs it uses are given by the column vector and input prices by the row vector . = [ 15,000 27,000 13,000] = [10 12 5] = [ 11,000 30,000] = [20 8] Using the given row and column vectors above, calculate the firm’s profit. using Cramer's rule

Cramer’s Rule as a method of systems of equations uses determinants with the same number of equations as variables. Determinants are the quantities that we obtain when we mathematically manipulate the elements of a square matrix.

Data and Calculations:

Matrix A:

A B C

Output units 15,000 27,000 13,000

Price of output 10 12 5

Sales revenue 150,000 324,000 65,000 (13,000 x 5)

Total Sales Revenue = 539,000 (150,000 + 324,000 + 65,000)

Matrix B:

A B

Input units 11,000 30,000

Cost per unit 20 8

Total cost 220,000 240,000 (30,000 x 8)

The Total Production Costs = 460,000 (220,000 + 240,000)

The profit can be calculated as the difference between the revenue and cost determinants to be equal to 79,000 (539,000 - 460,000).

Thus, using Cramer's Rule, the firm's profit is $79,000.

Learn more about Cramer's Rule here: https://brainly.com/question/15327191