Finding maximum output, profit and consumer surplus

[CollegeGuy]

I am struggling in college at the moment and I don't know where else to turn. Any assistance or advice would help, thank you
(a)

A firm’s short-run production function is given by Q = L2e-0.01L where Q = output and
L = labour. Find the value of L that maximises the average product of labour.





(b)

Using derivatives, show that the rule for profit maximisation is:



MR = MC and (MR)’ < (MC)’



Where MR = marginal revenue and MC = marginal cost.





(c)

Find the consumer’s surplus at Q = 8 for the demand function P = 100 – Q2.

 

[MarkFL]

...
(a)

A firm’s short-run production function is given by Q = L2e-0.01L where Q = output and
L = labour. Find the value of L that maximises the average product of labour...

Is this supposed to be:

$$Q=L^2-0.01L$$ ?

If so, there are several says to proceed. You could find the axis of symmetry, express in vertex form, or use differentiation. What have you tried so far?