How to find supply and demand

Question

Plant Touch This is doing market analysis for a new small beverage cup for hot drinks.

(a plant replacement for those white Styrofoam cups) made from garbanzo beans.

They have hired a consultant to help them project the demand for such a cup in their area.

The consultant has determined that demand should follow the function:

𝑝 = 𝐷(𝑞) =

780/q

Where p is the price of a carton of these cups (in dollars) and q is the quantity of cartons

Plant Touch This is able to determine for themselves how many cartons of cups they can

afford to supply. Their supply function is linear, and they know that at a price of $9 per

carton, they can supply 50 cartons per day, and at a price of $19 per carton, they can

supply 100 cartons per day.

1. Use algebra and your knowledge of linear functions to find the Supply function in

this scenario. (that has nothing to do with the Demand function from the

consultant) It is standard to use capital S as in 𝑝 = 𝑆(𝑞) for Supply – use that.

2. What is the slope of your linear supply function? What are the correct units for

that slope? Write a correct sentence in this scenario about what that slope is

telling you about these cups. In other words – what does this slope mean in the

scenario?

Answer 1

1. Because we are told to "use our knowledge of linear functions", we know the solution will take the form p=aq+c where p=price, q=quantity, and a & c are the slope and intercept.

We are told if p=9, q=50 & if p=19, q=100.

This means 9=50a + c & 19 = 100a + c

Now we have two equations with two variables and we can solve this.

From the first equation we can obtain that c=9-50a, then we can plug this into the second equation to get

19 = 100a + 9 - 50a. This becomes 10 = 50a, thus a = 1/5, and c = -1.

This means that the supply equation is p= 0.2q -1.