# Economics And Mathmatics

1- A multimedia company produces DVDs. It estimates their cost function to be:

**C(x)** = 12.2**x** + 48004.

The DVD is sold to retail outlets and the revenue function is:

**R(x)** = 17.13**x**.

Both **C(x)** and **R(x)** are in dollars and **x** = number of DVDs manufactured and sold.

How many DVDs must be manufactured and sold in order for the company to break even? (Round to the nearest whole number).

2- The same multimedia company as above revised their cost and revenue functions. Now they estimate:

**C(x)** = 12.6**x** + 48089 and **R(x)** = 18.19**x**.

Find the number of units that must be produced and sold for a profit of $242. (Round to the nearest whole number).

3- The same multimedia company now estimates their cost and revenue functions to be:

**C(x)** = 11.6**x** + 48001 and **R(x)** = 19.11**x**.

Find the profit of manufacturing and selling 9614 units. (Round to two decimal places).

4- In deciding whether to set up a new manufacturing plant, company analysts have decided that a linear function is a reasonable estimation for the total cost **C(x**) in dollars to produce x items.

They estimate the cost to produce 1,000 items/day as **$54745**, and the cost to produce 5,000 items/day as $**73731**.

Find the fixed cost. (Round to two decimal places).

5- A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy editing, typesetting) at $54382, and marginal costs (printing, paper, binding, shipping) at $1.6 for each book produced.

Suppose the book is sold to distributors for price of $10 each.

How many must be produced and sold for the publisher to break even? (Round to the nearest whole number).

6- Suppose that the supply function for honey is P = S(q) = 0.4 X + 1,

where p is the price in dollars for an 8-oz container and X is the quantity in barrels.

Find the quantity supplied at a price of $12 (Round to the nearest whole number).

7- **Suppose that the demand function for honey is P = D(q) = -1.5X + 64,**

**where p is the price in dollars for an 8-oz container and X is the quantity in barrels.**

**Find the price at a quantity demanded of 40 units. (Round to two decimal places).**

8- **Suppose that the demand function and supply function for honey are**

**P = D(q) = -1.5 X + 23 and P = S(q) = 0.3 X + 3.7**

**where p is the price in dollars for an 8-oz container and X is the quantity in barrels.**

**Find the equilibrium quantity. (Round to the nearest whole number).**

9- The manager of a T-shirt stand found that the cost to produce 10 T-shirts is $115.5, while the cost to produce 40 T-shirts is $397.3..

Assume the cost **C(x)** is a linear function of **x**, the number of T-shirts produced.

Calculate the marginal costs of a T-shirt, that is, the cost of producing one additional T-shirt. (Round to 2 decimal places)

10 The manager of a rival T-shirt stand found that her cost to produce 10 T-shirts is $112.04, while the cost to produce 40 T-shirts is $395.58..

Assume the cost **C(x)** is a linear function of **x**, the number of T-shirts produced.

Find the total cost of producing 100 T-shirts.(Round to 2 decimal places)

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