(Game Theory) In the subtraction game where players may subtract 1, 2 or 5 chips on their turn, identify the N- and P-positions. (Please do not forget to prove correctness of your answer.)

Autos orders their tires from a wholesaler. Every year Radfors requires 10,000 tires of a certain type. Cost is $150 per tire from their supplier.

The estimated cost of orderingat the suppliers and paying shipping fees is $80 per order. K = $80

The holding cost per tire is estimated to be 10% of the cost of the tire. h = .01 * $150 = $15

Using the economic ordering quantity model, the order size that would minimize the total costs is equal to

a. 103

b. 194

c. 287

d. 327

e. 10000

Current Issues

One of the biggest issues facing this company is the rise in prices of raw materials, especially the iconic almond, which due to drought in California has seen a price rise in recent years. In order to diversify their product line, Brown & Haley has started to expand its repertoire to including other nuts, such as cashews and macadamia nuts. They also have a project underway to test a new product line of packaged mixed nuts. Note that this scenario is fictional and the details do not represent actual operations of Brown & Haley.

The Scenario

The company is considering three nut mixes for inclusion in the new product line: Regular Mix, Deluxe Mix, and Holiday Mix. Each mix is made from 5 nuts in different combinations:

• The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, and 25% walnuts
• The Deluxe Mix consists of 20% of each type of nut
• The Holiday Mix consists of 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts

An accountant at Brown & Haley completed a cost analysis and determined that the profit contribution per pound is $1.65 for the Regular Mix, $1.90 for the Deluxe Mix, and $2.35 for the Holiday Mix.

Different nuts come from different suppliers. They are shipped in bulk containers and ordering a partial container is not possible. The currently available container sizes and costs are as follows:

One container of each of the types of nuts has been ordered and is on the way.

The sales and marketing teams have projected that initial demand for the different types of mixes will be as follows:

The president of Brown & Haley wants to commit to producing enough of the various mixes to meet the projected initial demand, even if not immediately profitable, in order to introduce these new mixes to the market.

The Analysis Required

The President would like to see a PowerPoint presentation of no more than 10 slides that answers the following questions:

1. How much of each type of mix should be made using only the nuts already ordered and keeping in mind the President’s requirement to meet the initial demand for each type of mix?  
2. Sometimes small amounts of certain types of nuts become available in secondary markets. Which types of nuts should be pursued in order to increase profit?
3. The marketing department is proposing an upgrade to the packaging of the Holiday Mix that would decrease the profit contribution from $2.35 to $2.29 per pound. Would the number of pounds of each type of mix be changed in the optimal solution? (Note that the President would be impressed if you did not need to rerun Solver to answer this question)
4. If the President’s requirement to meet the initial demand for each type of mix were eliminated would profitability be impacted? If so, by how much?

y'=(8x+2y)/(2x+8y)

(1) For each of the following statements, write its negation. Then prove or disprove the original statement.

(b) ∃x ∈ R, ∀y ∈ R, ∃z ∈ R, x² + y² + z² ≥ 1.

(c) ∀y ∈ N, ∃x ∈ N, y = 2x + 1.

(d) x ∈ R ⇒ x² ≥ 0.

(e) x ∈ [0, 1] ⇒ x > 2x − 1.

(f) For all real numbers x and y, x > y ⇔ x² > y²

Please answer all parts of the following question. Please show all work and all steps.

1a.) Solve the initial value problem W((t^2) + 1, f(t)) = 1, f(0) = 1

1b.) Let x1 and x2 be two solutions of x''+ ((x')/(t)) + q(t)x = 0, t > 0, where q(t) is a continuous function. Given that W(6)=7, find W(7)

1c.) Show that any solution of x''+ 5x' + 6x = 0 tends to zero as t approaches positive infinity.

1d.) Solve x'' + 2x' = 0, x(0) = 0, the limit as t approaches positive infinity x(t) = a

1e.) Solve x'' - x = t(e^(2t))

Honeydew bottles honey jars and sells them through retail channels. The weight on the sticker says 20 oz and Honeydew claims its bottles have a weight that is normally distributed with a mean of 20 oz and std dev of 2 oz. The retailer has been receiving several complaints lately and decides to measure a sample of 4 jars and finds weights of 18, 20, 17 and 19 oz respectively.
a. The retailer complains to Honeydew if he is 95% confident that the mean is lower than advertised. Does he complain?
b. If the retailer’s customers return any jar under 18 oz in weight, what fraction of the retailer’s sales result in a return?

c. Assuming Honeydew’s claim is true, what is their current sigma capability? What can they do to reduce the fraction of returns to 5%? What then would the new sigma capability be?

I WANT AN ABSOLUTELY CORRECT ANSWER WITH DETAILS.
PLS VERIFY BEFORE YOU POST

1. Let (X,d) be a metric space.

1. Show that every open d-ball is a d-open subset of X
2. Show that every closed d-ball is a d-closed subset of X.

2: Let (X,d) be a metric space. Show that a subset A of X is d-open if and only if it is the union of a (possibly empty) set of open d-balls.

Prove using mathematical induction: 3.If n is a counting number then 6 divides n^3 - n. 4.The sum of any three consecutive perfect cubes is divisible by 9. 5.The sum of the first n perfect squares is: n(n +1)(2n +1)/ 6

Suppose P, Q and R are atomic propositions.

(a) Show that the conjunction connective satisfies the commutative and associativity property.

(b) Show that the disjunction connective satisfies the commutative and associativity property.

(c) Construct a propositional form using all three atomic propositions above as well as the connectives conjunction, disjunction and conditional.

(d) Construct an equivalent propositional form for (c).

y''' −2y' −4y = 0, y(0) = 6, y'(0) = 3, y''(0) = 22

solve the initial value problem

You would convert it to m^3-2m-4=0. You find the root (m=2) and use synthetic division to find the other roots. m^2+2m+2 is what you get. I am stuck on what to do next?

y = 2e^(−x)*cosx−3e^(−x)*sinx + 4e^(2x) is the answer.

FlorU football programs are printed 1 week prior to each home game. Attendance averages 90,000 screaming and loyal Tators fans, of whom two-thirds usually buy the program, following a normal distribution with standard deviation of 5000 programs. A program sells for $4 each. Unsold programs are sent to a recycling center that pays 10 cents per program. The cost to print each program is $1.

a. How many programs should be ordered per game to maximize expected profit?

b. What is the stockout risk for this order size?

c. How sensitive is the order quantity in (a) to the following estimates?

I. The standard deviation of demand

II. The selling price of a program

III. The cost of recycling an unsold program Answer by considering at least 4 values of each quantity and calculating the corresponding order quantity. Draw a graph showing the effect of the above variables with order quantity on the Y axis. Comment briefly (1-2 lines) on each graph.

Sketch the graph of the following function: f(x) = x²+5x/25-x²
Make sure each solution has the following information with STEP BY STEP
Domain of f(x).
x-intercepts and y -intercepts. If x-intercepts are hard to compute, then ignore
them.
Vertical asymptotes.
Horizontal asymptotes.
Intervals where f is increasing and decreasing.
Local minima and local maxima.
Intervals where f is concave up and concave down.
Inflection points

You can use two types of fertilizer in your orange grove, Best Food and Natural Nutri. Each bag of Best Food contains 8 pounds of nitrogen, 4 pounds of phosphoric acid, and 2 pounds of chlorine. Each bag of Natural Nutri contains 3 pounds of nitrogen, 4 pounds of phosphoric acid and 1 pound of chlorine. You know that the grove needs at least 1,000 pounds of phosphoric acid and at most 400 pounds of chlorine. If you want to minimize the amount of nitrogen added to the grove, how many bags of each type of fertilizer should be used? How much nitrogen will be added?

Find f(1), f(2), f(3) and f(4) if f(n) is defined recursively by f(0)=4f(0)=4 and for n=0,1,2,…n=0,1,2,… by:
(a) f(n+1)=−2f(n)
f(1)=
f(2)=
f(3)=
f(4)=

(b) f(n+1)=4f(n)+5
f(1)=
f(2)=
f(3)=
f(4)=

(b) f(n+1)=f(n)²−4f(n)−2
f(1)=
f(2)=
f(3)=
f(4)=