# Business MathFinding maximum output, profit and consumer surplus

#### CollegeGuy

##### New member
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

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