given the weekly demand curve of a local wine producer is p= 50-0.1q, and that the total cost function is c= 1500+ 10q, where q bottles are produced each day and sold at a price of $p per unit. a)Express the weekly profit as a function of price. b) at what price must a bottle of wine be sold to realise maximum profit. c) what is the maximum profit that ca be made by the producer

a)the weekly profit as a function of price is

b) a bottle of wine be sold at $30 to realise maximum profit

c) the maximum profit that can be made by the producer is $2500

Step-by-step explanation:

The weekly demand curve of a local wine producer is p= 50-0.1q

p = price

q = quantity

Revenue function R =Price \times Quantity

R=(50-0.1q)q

Cost function: c= 1500+ 10q

Profit function=R(x)-C(x)

Profit function=

Profit function=   ----1

We have q = 500 - 10 p using p = 50 − 0.1q

General quadratic equation:

On comparing

a = -0.1 , b = 40 , c = -1500

Maximum Profit is at q =

To find price must a bottle of wine be sold to realise maximum profit

p= 50-0.1q

p= 50-0.1(200)=30

Substitute the value of q in profit function(1) get the maximum profit

So, Profit function=

Hence

a)the weekly profit as a function of price is

b) a bottle of wine be sold at $30 to realise maximum profit

c) the maximum profit that can be made by the producer is $2500

step-by-step explanation: