Consider a single source procurement situation: You have a demand rate of 151 units per period, replenishment rate of 2,550 units per period, lead time of 8 periods, item cost of 21.18, cost per procurement of 7.77, holding cost per unit of 7.63, and per unit shortage cost of 10.43. Find the minimum cost procurement quantity..

Solve : y''+2y'+y=e^-x + sinx by Undetermined Coefficients method and Variation of Parameters

Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x3 − 9x2 − 21x + 9

(a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.)

(b) Find the local minimum and maximum values of f. local minimum value local maximum value

(c) Find the inflection point. (x, y) = Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)

Consider the function f(x, y) = 4xy − 2x ⁴ − y ² .

(a) Find the critical points of f.

(b) Use the second partials test to classify the critical points.

(c) Show that f does not have a global minimum.

Let the cardinal number of N, the set of all natural numbers, be א0. Prove that the product set N × N = {(m,n);m ∈ N,n ∈ N} has the same cardinal number. Further prove that Q+, the set of all positive rational numbers, has the cardinal number N_0.

Hint: You may use the formula 2^(m−1)(2n − 1) to define a function from N × N to N, see the third example on page 214 of the textbook.

A 39-inch by 104-inch piece of cardboard is used to make an open-top container by removing a square from each corner of the cardboard and folding up the flaps on each side. What size square should be cut from each corner to get a container with the maximum volume? Enter the area of the square and do not include any units in your answer.

1. F=xi+yj+ (xz+yz)k, and Sis the part ofx+y+z= 1 in the first octant, oriented upwards. Compute∫∫Scurl(F)·dSdirectly.

2. Compute∫CF·drdirectly (3 curves to parameterize).

Using the formulas given in class for continuous and compound interest, show your calculated values for each investment below.

A) Placing $875 in an account giving 13.5% APR compounded daily for 2 years:

B) Placing $1000 in an account given 6.7% APR compounded continuously for 2 years:

C) Placing $1050 in an account giving 4.5% APR compounded monthly for 2 years:

D) RANK them in order from best (i.e. yielding the most interest) to worst (hint: compare either $ or % gain (APR)):

In your own words, describe why the graph of a rational function can cross its horizontal asymptote but it can never cross a vertical asymptote.

Find a solution of the following differential equations satisfying the given initial conditions

y''+y'+y=x² , y(0)=1, y'(0)=1

1. You’ve been hired by a company that makes rectangular storage containers. Each container has a square base and each container must have a volume of 10 m^3. The material for the base and top costs $6/m^2 and the material for the four sides costs $4/m^2. Find the dimensions of the container that minimize the cost of each container.

2. You want to impress your boss by creating a general strategy for finding the dimensions of the cheapest storage container given that the cost of material for the top and bottom is p dollars per square meter and the cost of the material for the sides is q dollars per square meter. As before, the storage container is rectangular, has a square base, and must have a volume of 10 m^3. Your dimensions will involve p and q.

For each part, you want to prove to your boss that these dimensions actually do minimize the cost.

Accordingly, you include an argument as to why these dimensions MUST minimize the cost.

What is the relation between definite integrals and area (if any)? Research and describe some other interpretations of definite integrals.

a)Find the value or values of c that satisfy the equation f(b)-f(a)/b-a = f′​(c)in the conclusion of the Mean Value Theorem for the function and interval. Round to the nearest thousandth.

f(x) ln(x-3), [4,7]

b)Suppose that

​c(x)=3x^3-40x^2+6844x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

c)A rectangular field is to be enclosed on four sides with a fence. Fencing costs $6 per foot for two opposite​ sides, and $5 per foot for the other two sides. Find the dimensions of the field of area 890fts^2that would be the cheapest to enclose

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 92 degrees occurs at 3 PM and the average temperature for the day is 85 degrees. Find the temperature, to the nearest degree, at 10 AM.

Please provide step by step how to find x after finding equation