Arrowhead is a manufacturing company that produces only one product, an electronic chip, and has provided the following data concerning its operations in January and February 2020:

January 2020 was the company’s first month of operations. The company has theoretical capacity to produce 1,200 chips a month without impacting any fixed costs. Since maintenance of the machines needs to be performed weekly, the company has practical capacity to produce 1000 chips a month. The company uses practical capacity as its denominator capacity level when determining a rate for its FMOH. The company uses FIFO inventory method for reporting purposes. All relevant costs are presented in the chart below and all estimated costs are equal to the actual costs incurred:

January 2020 February 2020

Selling price $400 $400

Chips in beginning FG inventory 0 200

Chips produced 800 800

Chips sold 600 600

Chips in ending FG inventory 200 400

Variable costs per unit:

    Direct materials $25 $25

    Direct labor $40 $40

    Variable manufacturing overhead $15 $15

    Variable selling and administrative $ 10 $ 10

Fixed costs:

    Fixed manufacturing overhead $120,000 $120,000

    Fixed selling and administrative $30,000 $30,000

A. What is the unit product cost for February 2020 under variable costing?

B. What is the unit product cost for February 2020 under absorption costing?

C. Create a contribution format income statement for February 2020. SHOW YOUR WORK. CLEARLY LABEL ALL STEPS.

D. What is the dollar value of the adjustment for product-volume variance to cost of goods sold (CGS) under absorption costing (if any) for February 2020? Don’t forget to indicate if this adjustment increases or decreases CGS.

Melisa was distraught. While her grandfather was getting on in years his loss had come as a shock late that Friday afternoon. She could think of no immediate family to contact and wandered her apartment wondering what to do. Finally at 9pm she realized she would have to do something so she called the closest funeral home to her grandfather ‘Lost Days Funeral Home’. Not expecting an answer so late she left a message hoping to hear back from them after the weekend. She was shocked to have the owner of Lost Days call her back within minutes. After 10pm on a Friday when most businesses should be closed! Susan (the owner of Lost Days) quickly put Melisa’s concerns to rest outlining a plan for the funeral (location and space for the religious service of her choice, cremation or burial of her grandfather, help with writing an obituary (article about her grandfather’s demise) and placing it in the local paper, organizing the wake (gathering of friends and family after the funeral), catering for the wake and even offered to help with a lawyer to assist in her role as executor (being responsible to act on the disposition of her grandfather’s possessions as outlined in his will). Now, instead of having a grief filled weekend with the stress of a funeral to arrange Melisa was now able to spend it recounting her fond memories of her grandfather.

based on the case study answer the following question:

Explain what you believe to be the need being satisfied, solution being offered or problem being solved by the funeral home from the purchaser’s perspective and why you believe this to be so.

Question:

1. Prove that the intersection of two compact sets is compact, using criterion (2).
2. Prove that the intersection of two compact sets is compact, using criterion (1).
3. Prove that the intersection of two compact sets is compact, using criterion (3).

Probably the most important new idea you'll encounter in real analysis is

the concept of compactness. It's the compactness of [a, b] that makes a

continuous function reach its maximum and that makes the Riemann in-

tegral exist. For subsets of R"h, there are three equivalent definitions of

compactness. The first, 9.2(1), promises convergent subsequences. The sec-

ond, 9.2(2) brings together two apparently unrelated adjectives, closed and

bounded. The third, 9.2(3), is the elegant, modern definition in terms of

open sets; it is very powerful, but it takes a while to get used to.

9.1. Definitions. Let S be a set in Rn. S is bounded if it is contained

in some ball B(0, R) about 0 (or equivalently in a ball about any point). A

collection of open sets {U} is an open cover of S if S is contained in U U(.

A finite subcover is finitely many of the Ua which still cover S. Following

Heine and Borel, S is compact if every open cover has a finite subcover.

9.2. Theorem. Compactness. The following are all equivalent conditions

on a set S in ]Rn.

(1) Every sequence in S has a subsequence converging to a point of S.

(2) S is closed and bounded.

(3) S is compact: every open cover has a finite subcover.

Criterion

(1)is the Bolzano-Weierstrass condition for compactness,

which you met for R in Theorem 8.3. The more modern Heine-Borel crite-

rion (3) will take some time to get used to. A nonclosed set such as (0, 1] is

not compact because the open cover {(1/n, oo)} has no finite subcover. An

unbounded set such as R is not compact because the open cover {(-n, n)}

has no finite subcover. This is the main idea of the first part of the proof.

Proof. We will prove that (3)->(2) -> (1) -> (3).

(3) ->(2). Suppose that S is not closed. Let a be an accumulation point

not in S. Then the open cover {{Ix - aI > 1/n}} has no finite subcover.

Suppose that S is not bounded. Then the open cover {{JxI < n}} has no

finite subcover.

(2) -> (1). Take any sequence of points in S C ]Rn. First look at just the

first of the n components of each point. Since S is bounded, the sequence

of first components is bounded. By Theorem 8.3, for some subsequence,

the first components converge. Similarly, for some further subsequence, the

second components also converge. Eventually, for some subsequence, all of

the components converge. Since S is closed, the limit is in S.

(1) =>. (3). Given an open cover {Ua}, first we find a countable subcover.

Indeed, every point x of S lies in a ball of rational radius about a rational

point, contained in some Ua. Each of these countably many balls lies in

some U,,. Let {Vi} be that countable subcover.

Suppose that {V} has no finite subcover. Choose xl in S but not in

V1. Choose X2 in S but not in V1 U V2. Continue, choosing xn in S but

not in U{V : 1 < i < n}, which is always possible because there is no finite

subcover. Note that for each i, only finitely many xn (for which n < i)

lie in V. By (1), the sequence xn has a subsequence converging to some

x in S, contained in some Vi. Hence infinitely xn are contained in Vi, a

contradiction.

9.3. Proposition. A nonempty compact set S of real numbers has a largest

element (called the maximum) and a smallest element (called the minimum).

Proof. We may assume that S has some positive numbers, by translating it

to the right if necessary. Since S is bounded, there is a largest integer part D

before the decimal place. Among the elements of S that start with D, there

is a largest first decimal place d1. Among the elements of S that start with

D.d1, there is a largest second decimal place d2. Keep going to construct

a = D.dld2d3.... By construction, a is in the closure of S.

Since S is closed, a lies in S and provides the desired maximum.

A minimum is provided by - max(-S).

Brighton investment is a Singapore resident company which had the following incomes for the year.

$

Trading profits in Singapore 1,500,000

Fixed deposit interest [UOB Singapore] 44,000

Gross royalty income for foreign countries:

- China 112,000

- Hong Kong 155,000

- Malaysia 35,000

- India 23,000

All the above foreign sourced income was remitted into Singapore on December 2019. Singapore has tax treaties with China, Malaysia and India but no treaty with Hong Kong. The withholding tax rates in foreign countries are: Malaysia - 8%

Hong Kong - 5.5%

China - 10%

India - 10%

Determine the final tax liability for Brighton Pte Ltd for the year of assessment 2020 after allowing the partial exemptions.

The values of certain types of collectibles can often fluctuate greatly over time. Suppose that the value of a particular limited edition figurine is found to be able to be modeled by the function

?(?) = −0.01?⁴ + 0.47?³ − 7.96?² + 49.18? + 65 for 0 ≤ ? ≤ 20 where ?(?) is in dollars, t is the number of years after the figurine was released, and ? = 0 corresponds to the year 1999.

a) What was the value of the figurine in the year 2009?

b) What was the value of the figurine in the year 2019?

c) What was the instantaneous rate of change of the value of the figurine in the year 2002?

d) What was the instantaneous rate of change of the value of the figurine in the year 2019?

e) Use your answers from parts a-d to estimate the value of the figurine in 2020.

American Products is concerned about managing cash efficiently. On the​ average, inventories have an age of

8484

​days, and accounts receivable are collected in

3939

days. Accounts payable are paid approximately

3333

days after they arise. The firm has annual sales of about

​$3737

million. Cost of goods sold are

​$2020

​million, and purchases are

​$1616

million.

a.  Calculate the​ firm's operating

cycle.

b.  Calculate the​ firm's cash conversion

cycle.

c.  Calculate the amount of resources needed to support the​ firm's cash conversion cycle.

d.  Discuss how management might be able to reduce the cash conversion cycle.

a. American​ Products' operating​ cycle, OC, is

nothing

days.  ​(Round to the nearest whole​ number.)

 Over the past 6​ years, Elk County Telephone has paid the dividends shown in the following​ table. he​ firm's dividend per share in

2020 is expected to be $1.27

2019 $1.22

2018 $1.17

2017 $1.12

2016 $1.08

2015 $1.04

2014 $1.00

a.  If you can earn 11​% on​ similar-risk investments, what is the most you would be willing to pay per share in 2019​, just after the $1.22 dividend?

b.  If you can earn only 8% on​ similar-risk investments, what is the most you would be willing to pay per​ share?

c.  Compare your findings in parts a and ​b, what is the impact of changing risk on share​ value?

Question 15 (1 point)

It is believed that students who begin studying for final exams a week before the test score differently than students who wait until the night before. Suppose you want to test the hypothesis that students who study one week before score greater than students who study the night before. A hypothesis test for two independent samples is run based on your data and a p-value is calculated to be 0.0428. What is the appropriate conclusion?

Question 15 options:

Question 16 (1 point)

You are looking for a way to incentivize the sales reps that you are in charge of. You design an incentive plan as a way to help increase in their sales. To evaluate this innovative plan, you take a random sample of your reps, and their weekly incomes before and after the plan were recorded. You calculate the difference in income as (after incentive plan - before incentive plan). You perform a paired samples t-test with the following hypotheses: Null Hypothesis: μ_D ≥ 0, Alternative Hypothesis: μ_D < 0. You calculate a p-value of 0.0542. What is the appropriate conclusion of your test?

Question 16 options:

Question 17 (1 point)

It is reported in USA Today that the average flight cost nationwide is $325.69. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually less than $325.69. The hypotheses for this situation are as follows: Null Hypothesis: μ ≥ 325.69, Alternative Hypothesis: μ < 325.69. If the true average flight cost nationwide is $300.92 and the null hypothesis is not rejected, did a type I, type II, or no error occur?

Question 17 options:

A newly issued bond pays its coupons once a year. Its coupon rate is 4.6%, its maturity is 10 years, and its yield to maturity is 7.6%.

a. Find the holding-period return for a one-year investment period if the bond is selling at a yield to maturity of 6.6% by the end of the year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Holding-period return 14.9 %

b. If you sell the bond after one year when its yield is 6.6%, what taxes will you owe if the tax rate on interest income is 40% and the tax rate on capital gains income is 30%? The bond is subject to original-issue discount (OID) tax treatment. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

c. What is the after-tax holding-period return on the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

After-tax holding-period return 9.67 %

d. Find the realized compound yield before taxes for a two-year holding period, assuming that (i) you sell the bond after two years, (ii) the bond yield is 6.6% at the end of the second year, and (iii) the coupon can be reinvested for one year at a 2.6% interest rate. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Realized compound yield before taxes 10.57 %

e. Use the tax rates in part (b) to compute the after-tax two-year realized compound yield. Remember to take account of OID tax rules. (Do not round intermediate calculations. Round your answer to 2 decimal places.)