Assume that each situation can be expressed as linear cost function. Find the cost function in each case.
Marginal cost $90;150items cost $16,000 to produce.
this is what i end up.
c(x)=90x-11900
That is correct if the cost function is linear, which is probably what your teacher wanted. However, in reality, the cost funtion is seldom linear. Cost per item diminishes usually with volume.
To find the cost function in this case, we need to use the given information.
We know that the marginal cost is $90, which means that for each additional item produced, the cost increases by $90.
We also know that it costs $16,000 to produce 150 items.
To find the cost function, we can start by finding the initial cost. The initial cost is the cost to produce 0 items. We can calculate this by subtracting the cost of producing 150 items (given) from the total cost at 150 items.
Initial cost = Total cost at 150 items - Cost of producing 150 items
Initial cost = $16,000 - ($90 * 150)
Initial cost = $16,000 - $13,500
Initial cost = $2,500
Now that we have the initial cost, we can write the cost function. Since the marginal cost is $90, the cost function will be in the form of c(x) = mx + b, where m is the slope (marginal cost) and b is the initial cost.
Therefore, the cost function for this situation is:
c(x) = $90x + $2,500