Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 220 grams of protein and at least 180 grams of fat. If chicken costs 11¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost? HINT [See Example 4.] (If an answer does not exist, enter DNE.)

Linear Programming Problem 1:

George's Woodcarving Company manufactures two types of wooden toys: soldiers and trains. A soldier sells for $27 and uses $10 worth of raw materials. Each soldier manufactured increases George's variable labor and overhead costs by $14. A train sells for $21 and uses $9 worth of raw materials. Each Train built increases George's variable labor and overhead costs by $10. The manufacture of wooden soldiers and trains requires two types of skilled labor: carpentry and finishing. A soldier requires 3 hours of carpentry labor and 2 hours of finishing labor. A train requires 4 hours of carpentry labor and 1 hour of finishing labor. Each week, George's can obtain all the needed raw material but only 240 carpentry hours and 100 finishing hours. Demand for trains is unlimited, but at most 28 soldiers are bought each week. George wishes to maximize weekly profit (revenue – costs). The company wants to find out the optimal production strategy that maximizes the weekly profit.

First solve this problem graphically or using the Solver. Have the solved graph or spreadsheet ready. For graphical approach, you need to solve for the optimal solution by solving simultaneous equations after graphing.

Then answer the quiz questions.

1. How many decision variables are in this problem?

2. How many finishing hours are available in this problem?

3. What is the unit profit of a toy soldier? $____.

4. To produce 5 toy soldiers and 5 toy trains, how many carpentry hours are required?

5. To produce 5 toy soldiers and 10 toy trains, how many finishing hours are required?

6. In the optimal solution, how many toy soldiers are produced?

7. In the optimal solution, how many toy trains are produced?

8. What is the maximum total profit?

9. In the optimal solution, how many hours of carpentry labor in total are used?

10. In the optimal solution, how many hours of finishing labor in total are unused?

Let f and g be two functions whose first and second order derivative functions are continuous, all defined on R. What assumptions on f and g guarantee that the composite function f ◦g is concave?

1.  Inventory Management

Williams & Sons last year reported sales of $145 million, cost of goods sold (COGS) of $120 and an inventory turnover ratio of 5. The company is now adopting a new inventory system. If the new system is able to reduce the firm's inventory level and increase the firm's inventory turnover ratio to 8 while maintaining the same level of sales and COGS, how much cash will be freed up? Do not round intermediate calculations. Round your answer to the nearest dollar.

ANSWER: $  

2. Receivables Investment

Medwig Corporation has a DSO of 37 days. The company averages $4,250 in sales each day (all customers take credit). What is the company's average accounts receivable? Round your answer to the nearest dollar.

ANSWER: $

3. Cost of Trade Credit

What are the nominal and effective costs of trade credit under the credit terms of 1/20, net 30? Assume 365 days in a year for your calculations. Round your answers to two decimal places. Do not round intermediate calculations.

ANSWER: (percentages)

Nominal cost of trade credit:

Effective cost of trade credit:

4. Cost of Trade Credit

A large retailer obtains merchandise under the credit terms of 3/20, net 30, but routinely takes 65 days to pay its bills. (Because the retailer is an important customer, suppliers allow the firm to stretch its credit terms.) What is the retailer's effective cost of trade credit? Assume 365 days in year for your calculations. Do not round intermediate calculations. Round your answer to two decimal places.

ANSWER: (percentage)

5. Accounts Payable

A chain of appliance stores, APP Corporation, purchases inventory with a net price of $250,000 each day. The company purchases the inventory under the credit terms of 2/15, net 40. APP always takes the discount, but takes the full 15 days to pay its bills. What is the average accounts payable for APP? Round your answer to the nearest dollar.

ANSWER: $

Consider a rocket that burns steadily. The higher pressure in the combustion chamber, the faster the propellant burns. Why is this? The relationship is such that the higher the pressure, the closer the gaseous flame is to the surface and the more effectively it can transfer heat back to the surface thereby gasifying the propellant quicker. The rate of gas generation, ?_? , can be described by the equation: ?_?=?_1 ?^?, where P is the pressure, and C1 and n are the constants for a given propellant with given exposed surface area.

The hot gas leaving the rocket must pass through the throat of the exhaust nozzle at sonic velocity.

▪The higher the pressure, the greater the density of this gas and the greater the rate of mass flow at sonic velocity. (The speed of sound in a gas is independent of pressure.) Accordingly, the rate of gas escape, ??r_e , is described by the equation: ??=?2?r_e=C_2 P where C2 is a constant, dependent on cross section area of the nozzle throat and on the velocity of sound in the combustion products.

▪What is the steady operating pressure of a solid-propellant rocket for the given values of the constants C1 , C2, and n? What values of n keep it stable?

PLEASE WRITE CLEARLY AND EXPLAIN WHY IS THE ANSWER THE WAY IT IS PLEASE THANK YOU

Explain the difference between simple and compound interest and describe a scenario when the benefits of one outweighs the other. Provide specific examples.

Find the Green's function for each of the following problem, and determine
the solution of each of the following boundary-value problem:
y" + 4y = e^x
y(0) = 0
y'(1) = 0

In the 3-month period November 1, 2014, through January 31, 2015, Hess Corp. (HES) stock decreased from $80 to $64 per share, and Exxon Mobil (XOM) stock decreased from $96 to $80 per share.† If you invested a total of $25,920 in these stocks at the beginning of November and sold them for $21,120 3 months later, how many shares of each stock did you buy?

For the Poincare plane, find two lines L1 and L2 and a point P off each such that through P there are exactly two lines parallel to both L1 and L2.

Give an example of proof by construction.

For example, prove that for every well-formed formula f in propositional logic, an equivalent WFF exists in disjunctive normal form (DNF).
HINT: Every WFF is equivalent to a truth function, and we can construct an equivalent WFF in full DNF for every truth function. Explain how.

A recent college graduate buys a new car by borrowing $22,000 at 8.4%, compounded monthly, for 4 years. She decides to pay $552 instead of the monthly payment required by the loan.

(a) What is the monthly payment required by the loan? (Round your answer to the nearest cent.)
$  

How much extra did she pay per month? (Round your answer to the nearest cent.)
$  

(b) How many $552 payments will she make to pay off the loan? (Round your answer up to the next whole number.)
payments

(c) How much will she save by paying $552 per month rather than the required payment? (Round your answer to the nearest cent.)
$

Find the eigenvalues and eigenfunctions of the Sturm-Liouville system
y"+ lamda y = 0 o<x<1
y(0) = 0
y'(1) = 0
(b) Show that the eigenfunctions Yn and Ym you obtained from the above
are orthogonal if n not= m.

factoring ax^2+bx+c with Grouping, Box Method, Star Method/Diamond Method/X-method, and Tic-Tac-Toe Method (with a>1)

1) What is the linear density in denier if 1.75 pound of yarn has a length of 110 miles?

2) How many 3.8 micronaire fibers will be in the cross-section of a 125 denier yarn?

3) If you want to make a yarn trail around a rectangular field that is 11 feet by 17 feet, what yarn mass would you need in grains if the yarn has a linear density of 55 tex?

4) How many 36 tex fibers are in the cross-section of a 65 gr/yd sliver?

5) What is the length in kilometers of 113.6 pounds of 12 ktex yarn?

6) How many 4.5 dtex fibers are in the cross-section of a 49 grain/yd sliver?

7) What is the linear density of a yarn in ktex if 0.5 miles of yarn weighs 41400 grains?

8) What is the mass in milligrams of 250 fibers in each fiber has a linear density of 3.4 denier and a length of 2.7 inches?

uniformly convergent, Analysis

how sup(fn(x)-f(x))

and fn(x)-f(x)

I don't understand how to transform from sup(fn(x)-f(x)) to fn(x)-f(x) to represent uniformly convergent

Also, please kindly draw the picture to explain sup(fn(x)-f(x))

sup=supremum