Question

24. Given MR = 200-4X, and MC = 50 + 2X, and the total cost of producing 10 widgets is $700. At what level should the company hold production (X=#units produced) in order to maximize the profits?

Answer 1

Solution-

We have

Marginal revenue MR=200 –4x

Marginal cost MC=50 +2x

The profit is increased upto when marginal revenue is greater than marginal cost.It means the revenue generated from producing one more item is greater than the cost raises from selling one more item.

For maximum profit ,marginal revenue is equal to marginal cost.

So, MR = MC

Or 200 –4x = 50 +2x

Bringing like terms on the same side-

–4x–2x = 50 –200

Combining the like terms

–6x =–150

Or x= -150 /(-6)

Or x=25

Hence for maximum profit , the the production must be x= 25 units