A manufacturing company makes transistors for which it has the following demands function, where p is price in

Question

euros a q is quantity in thousands of units.

p = 640 - 30q

The manager of the company has determined that fixed costs are €450 and variable costs are €80 per thousand transistors made.

a) Write down the total cost function for transistors.

b) Determine the profit function for transistors and determine the root(s) if any for this function.

C) How many transistors should be made in order to maximise profit?

d) What is the selling price of a single transistor when profit is maximised?

e) What is the value of maximum profit

p.s. I would know how to do this if i had the TC but because i don't have the TC, i dont have a clue on what to do. can somebody please help me out on this?? I'm preparing for my resit exam, i really need to understand this. Thanks in advance

Answer 1

I would suggest that Total Cost = Fixed Cost + Variable Cost .. (you MUST know this already ?)

a) TC = 450 + 80 * Q

[where Q= Quantity produced in thousands]

Wasn't so hard, was it  :-) ?

b) I assume you know that Profit = Revenue - Costs ?

Revenue = Price * Quantity ... you have been given the Price function (640- 30 * Q) .. so you have the formula :-

Profit = (640- 30 * Q) * Q    -   (450 + 80 * Q)

I leave you to do the maths ..

c)  Differentiate the function above ..

d) Qty. answer from (c) plugged into profit function given ..

e) (c) * (d)