MATEMATİK I

Break-even point is the point where the total cost and the total revenue are equal C(x)=R(x).

For our question, R(x)=p*x=3x and C(x)=v*x+a=1,5x+2750. 

1,5x+2750=3x,   1,5x=2750,   x=1833,33. The answer is B.

Once again price elasticity of demand is

The answer is A.

The total revenue function for the product is,

R(x)=p*x=10-(2x/4)*x=10x-2(x^2)/4

Since the total profit is the difference between the total revenue and the total cost function we have

The answer is C.

We first find the equilibrium point by equating the supply and demand functions. Therefore, the equality 

-5x+500=2x-200

gives

7x=700,   x=100

Since there will be a shortage in the market, to the left o this point the correct answer x<100. The answer is E.

in the simplest terms the definition of demand tells us the desire or willingness of a customer to pay a certain price for a particular item she wants to buy. Suppose that the seasonal price of a pair of sneakers is 180 TL. The same sneakers cost 100 TL in the discount season. A customer therefore may prefer to buy it at the discount season, and even maybe buys two pairs instead of one pair. Therefore, demand is proportional to the price of the goods.

The point where the quantity demanded equals the supply provided is called the equilibrium point.

The break-even point is the point at which cost or expenses and revenue are equal: there is no net loss or gain, and one is said to have “broken even.”

The additional cost needed to produce or purchase one more unit of a good or service is called the marginal cost. It corresponds to the derivative of the total cost function C(x).

If the company wants to make a profit of 2500TL then the profit function must be equal to this quantity. In other words,

P(x)= 2500 ⇒ 80 x−4400=2500⇒80 x=6900 so that
x=86,25 units.

If demand is elastic, i.e. |E_p|>1, revenue R(p)=p q(p) decreases as price p increases.
If demand is inelastic, i.e. |E_p|<1, revenue R increases as price p increases.
If demand is of unit elasticity, i.e. |E_p|=1, revenue is unaffected by a small change in
price.

Let x denote the number of items produced and sold. The total revenue is
R (x) = 130 x

and the total cost is
C (x) = 50 x + 4400

To find the break-even point we equate total cost to total revenue, so

C(x)=R(x)⇒ 50 x+4400=130 x⇒80 x=4400
so that
x =55
Thus, the manufacturer has to sell at least 55 units to break even, i.e. no profit, or no loss.

let x denote the demand and p the price of the product. We are given (x₁,p₁)=2000,1200) and (x2, p2)=(3000,1000), since there is TL discount in the price. The demand line that passes through these points has slope m=-1/5 and its equation is p=-x/5 +1600

If demand is of unit elasticity, i.e. |E_p|=1, revenue is unaffected by a small change in price.

The profit function we would like to maximise is P(x)=R(x)−C(x)
R(x)=x p(x)=x ⋅(200−3x)=200x −3x²

so that

P(x)=−2x ² +120x−75
To find the maximum price, let us take the derivative of P(x) and equate it to zero:

P'(x)=−4x+120 = 0 ⇒ x=30