Question

How do you write the expression for cost, given that a company's total cost to produce shirts is $\$100$ plus $\$7$ per shirt?

Answer 1

Hint: In this question we have been given with a world problem. In order to find a solution to this problem, we will have to first convert this word problem into mathematical format and then after converting into mathematical form, we will have to create an equation or expression which satisfies the given conditions in the question.

Complete step-by-step solution:
We know that the company’s total cost to produce shirts is $\$100$ plus $\$7$ per shirt.
This implies that the cost $\$100$ is fixed for every case of the manufacturing of shirts and is not dependent on the number of shirts produced.
Let $y$ be the total cost of construction of shirts. Since the cost $\$100$ is fixed we have the cost as:
$\Rightarrow y=\$100$
Now we know that the cost of producing a shirt is $\$7$. And since this cost is dependent on the number of shirts which are to be produced, we need a variable which represents the number of shirts which are to be produced.
Let the number of shirts which are to be produced be $s$.
Now the cost of producing $1$ shirt is $\$7$ therefore, the cost of producing $s$ number of shirts will be $s$ multiplied by $\$7$ which can be written mathematically as $s\times \$7$
Now on adding the costs we get:
$\Rightarrow y=\$100+\left(s\times\$7\right)$
On taking the unit of currency common, we get:
$\Rightarrow y=\left( 100+7s \right)\$$, which is the required solution.

Note: It is to be remembered that this is a word problem which describes a real-life scenario. In general terms the cost $\$100$ is called the ‘overhead cost’ and $\$7$ is called the ‘actual cost’. The total cost of manufacturing will depend on the number $s$, if it is high then the cost would be high and if it is low then the total cost will be low, but the overhead cost will be the same.