When we differentiate and assign the derivative to zero.

Hence,

and , so

So profit is maximised when the output (q) is set to 10

Now, let us consider how we can investigate the model as a case study.

The profit model is made up of two distinct sections i.e. Revenue and Costs. Revenue is based upon the linear demand equation and linear demand, consists of an intercept term and a slope term.

Costs on the other hand, consist of two distinct entities i.e. a Fixed Cost (the cost of maintaining a business irrespective of level of output) and, a Variable Cost (the additional costs associated with changes in output).

If we consider Revenue, then we are considering the product of the linear demand equation and output ('q'). We know that the linear demand equation consists of an intercept term and a slope term.

Hence by creating changes in the coefficients associated with the linear demand equation, we can create changes in the Revenue equation. So, we can change the value of the Intercept term and/or the Slope term.

Changes in either will create changes in the Revenue equation.

Creating changes in the revenue equation will ultimately create changes in the Profit equation!

Similarly, the cost equation consists of a fixed cost and a variable cost. Changes in either will cause changes in the Profit equation.

Hence, the case study analysis is set up as follows: we will consider changes in the Fixed Cost, then changes in the Variable Cost, followed by changes in the intercept term and then in the slope term of the linear demand equation.

Speaking about changes in the Fixed Cost look at graphs changes. Simply vertically moves the position of the graph of the equation. In the case of the Profit graph, a decrease in the...

), i.e. the minus sign outside the brackets of the TC effectively changed the sign of every term within the brackets when the brackets were removed!

So 000 is our profit equation! Notice how it represents a quadratic equation with a negative sign in front of the 'squared' term. Such an indication tells us that we are looking at a MAXIMUM point. Let us plot a graph of our profit equation!

Costs on the other hand, consist of two distinct entities i.e. a Fixed Cost (the cost of maintaining a business irrespective of level of output) and, a Variable Cost (the additional costs associated with changes in output).

Hence by creating changes in the coefficients associated with the linear demand equation, we can create changes in the Revenue equation. So, we can change the value of the Intercept term and/or the Slope term.

Hence, the case study analysis is set up as follows: we will consider changes in the Fixed Cost, then changes in the Variable Cost, followed by changes in the intercept term and then in the slope term of the linear demand equation.

Speaking about changes in the Fixed Cost look at graphs changes. Simply vertically moves the position of the graph of the equation. In the case of the Profit graph, a decrease in the value of the fixed costs moves the profit graph upwards (and vice versa).

Hence, the constant values (-2,000 and 150 in this case) are technically
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