please make sure you answer the question in full and don\'t leave anything blank

Question

please make sure you answer the question in full and don't leave anything blank.

3. A firm uses a single input to produce a good according to the production function q f)- 4x, where is x is the number of units of input. The commodity sells for $100 per unit. The input costs $50 per unit. a. Write down a function that state the firm's profit as a function of the amount of input x. output? c. How much profit will this firm make? b. What is the profit maximizing amount of input.x? What is the profit maximizing amount of

Explanation / Answer

a) Profit = total revenue - total cost

= price x quantity - cost of input

= 100q - 50x

= 100*(4x^0.5) - 50x

= 400x^0.5 - 50x

b) Maximize the profit

dPR/dx = 0

400*0.5*x^(-0.5) = 50

x^0.5 = 4

x* = 16

Hence profit maximizing level of input of x is 16. Output is 4*(16^0.5) = 16

c) Profit = 400*(16^0.5) - 50*16 = 800

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