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The cost function for the Seattle factory is given by the following piecewise function. That is, ()is the cost function, where is the number of units produced. The plant’s maximum capacity is 42,000 units per day. () = { 0.35 ≤ 8,000 0.75 8,000 < ≤ 20,000 0.83 − ( 200,000) 20,000 < ≤ 42,000



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The cost function for the Seattle factory, denoted as C(x), is given by the following piecewise function:

C(x) = { 0.35x , for 0 < x ≤ 8000

0.75x , for 8000 < x ≤ 20000

0.83x - (20000), for 20000 < x ≤ 42000

In this cost function:

For the first 8000 units produced, the cost per unit is $0.35.

For the next 12000 units (from 8001 to 20000 units), the cost per unit is $0.75.

For the rest of the units (from 20001 to 42000 units), the cost per unit is $0.83 but reduced by a fixed $20000.

This cost function represents the variable cost per unit produced at different production levels, up to the plant's maximum capacity of 42000 units per day.

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