The problem asks to create a linear cost function $C(x)$ for a company, where $x$ is the number of items produced in a month. The fixed cost is K1,250 per month, and the production cost is K37.50 per item. Then, the problem asks to calculate the monthly cost for producing 100 items.

1. Problem Description

The problem asks to create a linear cost function $C(x)$ for a company, where $x$ is the number of items produced in a month. The fixed cost is K1,250 per month, and the production cost is K37.50 per item. Then, the problem asks to calculate the monthly cost for producing 100 items.

2. Solution Steps

The total cost $C(x)$ is the sum of the fixed cost and the variable cost (production cost per item multiplied by the number of items).

The fixed cost is K1,

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0. The variable cost is K37.50 per item, so for $x$ items, it is $37.50x$.

Therefore, the linear cost function is:

$C(x) = 1250 + 37.50x$

To calculate the monthly cost for producing 100 items, we substitute $x = 100$ into the cost function:

$C(100) = 1250 + 37.50(100)$

$C(100) = 1250 + 3750$

$C(100) = 5000$

3. Final Answer

The linear cost function is $C(x) = 1250 + 37.50x$.

The monthly cost for producing 100 items is K5,000.