Question

It costs a company $58 to produce 6 units of products and $78 to produce 10 units of products. Assuming that the cost function is linear, how much does it cost to produce 25 units?

a) Various cost values
b) $150
c) $168
d) $200

Answer 1

To find the cost to produce 25 units, we can set up a linear equation using the given data points. Solving this equation will give us the cost per unit, which we can then multiply by 25 to find the total cost.

Step-by-step explanation:

To find the cost to produce 25 units, we can first find the cost per unit. We have two data points: it costs $58 to produce 6 units and $78 to produce 10 units.

We can set up a linear equation using the slope-intercept form, y = mx + b, where y represents the cost and x represents the number of units.

Using the first data point, we have 58 = 6m + b. Using the second data point, we have 78 = 10m + b.

Solving these equations simultaneously, we find that m = 5 and b = 28.

Now we can plug in x = 25 into the equation to find the cost: y = 5(25) + 28 = 125 + 28 = 153. Therefore, it costs $153 to produce 25 units of products.