Please answer full questions 13 Please make answers clear an

***Please answer full questions 1-3. Please make answers clear and readable. Thank you!***

1. A company charting its profits notices that the relationship between the number of units sold, x, and the profit, P, is linear. If 190 units sold results in $380 profit and 240 units sold results in $2980 profit, write the profit function for this company.

P =

Find the marginal profit.
$

2. Find the equilibrium point for the following supply and demand functions.

Demand:     p = 3q + 190
Supply:     p = 15q + 10
(q, p) =

3.A group of retailers will buy 72 televisions from a wholesaler if the price is $325 and 112 if the price is $275. The wholesaler is willing to supply 64 if the price is $240 and 144 if the price is $330. Assuming the resulting supply and demand functions are linear, find the equilibrium point for the market.

(q, p) =

Solution

Solution :-(1) If x = number of units. y = profit.

So our points are (190,380) and (240,2980)

Slope = m = (Change in Y) / Change in X.

So we have slope , m = 2600/50 = 52

We know equation of line , y = mx + b

====> y = 52x + b

Let us use the point (190,380)

So 380 = 52(190)+b ===> 380 = 9880 + b == > b = - 9500

So the profit function P(x) = 52x - 9500

This is the required solution of the equation.