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ISEE Middle Level
Mathematics Achievement

Profit from T-shirt Production Inequality

Medium Algebra Inequalities

A company manufactures custom t-shirts. The cost to produce each t-shirt is represented by the inequality:

$$C(x) = 5x + 200$$

where $$C(x)$$ is the total cost in dollars and $$x$$ is the number of t-shirts produced. To ensure that the company makes a profit, the cost must be less than the revenue generated by selling the t-shirts:

$$R(x) = 15x$$

where $$R(x)$$ is the total revenue in dollars. To find the number of t-shirts that must be produced to maintain a profit, solve the inequality:

$$C(x) < R(x)$$

What is the maximum number of t-shirts that can be produced while still making a profit?

Hint

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