economics and mathmatics
Xnunux
AmultimediacompanyproducesDVDs.docx1- A multimedia company produces DVDs. It estimates their cost function to be:
C(x) = 12.2x + 48004.
The DVD is sold to retail outlets and the revenue function is:
R(x) = 17.13x.
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) = 12.6x + 48089 and R(x) = 18.19x.
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) = 11.6x + 48001 and R(x) = 19.11x.
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.
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)
