Question

For a certain company, the cost function for producing x items is C(x)=50x+250

and the revenue function for selling x items is R(x)=−0.5(x−120)2+7,200
. The maximum capacity of the company is 170
items.

Profit when producing 70
items=?
Profit when producing 80
items=?

Can you explain, from our model, why the company makes less profit when producing 10 more units?

Answer 1

Profit when producing 70 items = $3,050

Profit when producing 80 items = $1,350

Explanation:

To find the profit when producing a certain number of items, we need to subtract the cost from the revenue:

Profit = Revenue - Cost

Let's calculate the profit for producing 70 items:

Revenue when producing 70 items:

R(70) = -0.5(70-120)^2 + 7,200 = $6,800

Cost of producing 70 items:

C(70) = 50(70) + 250 = $3,750

Profit when producing 70 items:

Profit = Revenue - Cost = $6,800 - $3,750 = $3,050

Similarly, let's calculate the profit for producing 80 items:

Revenue when producing 80 items:

R(80) = -0.5(80-120)^2 + 7,200 = $5,600

Cost of producing 80 items:

C(80) = 50(80) + 250 = $4,250

Profit when producing 80 items:

Profit = Revenue - Cost = $5,600 - $4,250 = $1,350

We can see that the profit is less when producing 10 more units because the cost of producing those additional units exceeds the revenue generated from selling them. In other words, the marginal cost (the cost of producing one additional unit) is greater than the marginal revenue (the revenue generated from selling one additional unit) beyond a certain point.

This is an example of the law of diminishing returns, which states that as we increase the quantity of inputs while keeping other inputs constant, the marginal product (output per unit of input) eventually decreases.

Hope this helps!