Question

Solve the equations below using the Gaussian Elimination Method:

2x+3y−16z=1
x+2y−3z=0
2y−z=0
​ If the fixed costs are 25 , variable costs per unit are 2 and the price function is p(x)=20−x,x is the quantity of product.
1. What is a profit function?
2. Find the levels of output which give a profit of 31 .
3. Find the maximum profit and the value of x at which it is achieved.

Answer 1

The profit function is calculated by subtracting the total cost from the revenue. To find the profit function, multiply the quantity with the price and deduct the sum of fixed costs and variable costs per unit. To find the levels of output giving a profit of 31, set the profit function equal to 31. To find the maximum profit and the value of x, use calculus to find the maximum point of the profit function.

Step-by-step explanation:

The profit function is given by the formula:

Profit = Revenue - Total Cost

To find the profit function, we need to determine the revenue and total cost functions. The revenue function is calculated by multiplying the quantity of product, x, with the price function, which in this case is p(x) = 20 - x. The total cost function is calculated by adding the fixed costs (25) to the variable costs per unit (2x).

1. Profit function: Profit = (20 - x)x - (25 + 2x)

2. To find the levels of output which give a profit of 31, we set the profit function equal to 31 and solve for x.

3. To find the maximum profit and the value of x at which it is achieved, we can use calculus to find the maximum point of the profit function.