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VladimirAG [237]
2 years ago
11

The table below shows how total donations, average donations, total labor costs and average labor costs vary depending on the nu

mber of employees State U hires for its fundraising activities. Number of Employees Total Donations Average Donations Total Labor Costs Average Labor Costs 1 $30,000 $8,000 2 $42,426 $17,000 3 $17,321 $27,000 4 $60,000 $9,500 5 $13,416 $50,000 The Chair of the Economics Department at State U says that fundraising employees should be hired as long as their marginal benefit exceeds their marginal cost. If the University follows this advice, then ______ employee(s) will hired, and the net benefit (total donations minus total labor costs) will be ______.
Business
1 answer:
dlinn [17]2 years ago
4 0

Answer:

2 employees will be hires and net benefits will $25,426

Explanation:

I have attached an excel for perusal.

In it i have calculated the missing figures,but please note the formulas i have used as stated as below:

Total costs= Average costs* number employees

Total donations= average donations*number of employees

Average costs=total costs /number of employees

Average revenue =total donations /number of employees

Marginal cost=Total costs at higher range-Total costs at lower range/(Number of employees at higher range -Number of employees at lower range)

Marginal donations=Total donations at higher range-Total donations at lower range/(Number of employees at higher range -Number of employees at lower range)

Download xlsx
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Each machine must be run by one of 19 cross-trained workers who are each available 35 hours per week. The plant has 10 type 1 ma
Mrac [35]

Answer:

The Linear programming model is given as below

Profit Function: P=90X+120Y+150Z

Constraints:

2X+2Y+Z\leq 400

3X+4Y+6Z\leq 240

4X+6Y+5Z\leq 320

\dfrac{2X+2Y+Z}{40}\leq 10

\dfrac{3X+4Y+6Z}{40}\leq 6

\dfrac{4X+6Y+5Z}{40}\leq 8

\dfrac{2X+2Y+Z}{35}+\dfrac{3X+4Y+6Z}{35}+\dfrac{4X+6Y+5Z}{35}\leq 19

Explanation:

As the question is not complete, the complete question is found online and is attached herewith.

Let the number of product 1 to be produced is X, that of product 2 is Y and product 3 is Z

so  the maximizing function is the profit function which is given as

P=90X+120Y+150Z

Now as the number of hours in a week are 40 and there are a total of 10 type 1 machines so the total number of machine 1 hours are 40*10=400 hours

As from the given table product 1 uses 2 machine hours of machine 1, product 2 uses 2 machine hours of machine 1 and product 3 uses 1 hour of machine 1 so

2X+2Y+Z\leq 400

Now as the number of hours in a week are 40 and there are a total of 6 type 2 machines so the total number of machine 2 hours are 40*6=240 hours

As from the given table product 1 uses 3 machine hours of machine 2, product 2 uses 4 machine hours of machine 2 and product 3 uses 6 hour of machine 2 so

3X+4Y+6Z\leq 240

Now as the number of hours in a week are 40 and there are a total of 8 type 3 machines so the total number of machine 3 hours are 40*8=320 hours

As from the given table product 1 uses 4 machine hours of machine 3, product 2 uses 6 machine hours of machine 3 and product 3 uses 5 hour of machine 3 so

4X+6Y+5Z\leq 320

Now as the machine 1 is used as 2X+2Y+Z in a week and the week is of 40 hours so the number of machines to be used are given as

\dfrac{2X+2Y+Z}{40}\leq 10

Now as the machine 2 is used as 3X+4Y+6Z in a week and the week is of 40 hours so the number of machines to be used are given as

\dfrac{3X+4Y+6Z}{40}\leq 6

Now as the machine 3 is used as 4X+6Y+5Z in a week and the week is of 40 hours so the number of machines to be used are given as

\dfrac{4X+6Y+5Z}{40}\leq 8

Now the workers are available for 35 hours so the worker available at the machine 1 is given as

\dfrac{2X+2Y+Z}{35}

That of machine 2 is given as

\dfrac{3X+4Y+6Z}{35}

That of machine 3 is given as

\dfrac{4X+6Y+5Z}{35}

As the total number of workers is 19 so the constraint is given as

\dfrac{2X+2Y+Z}{35}+\dfrac{3X+4Y+6Z}{35}+\dfrac{4X+6Y+5Z}{35}\leq 19

So the Linear programming model is given as below

Profit Function: P=90X+120Y+150Z

Constraints:

2X+2Y+Z\leq 400

3X+4Y+6Z\leq 240

4X+6Y+5Z\leq 320

\dfrac{2X+2Y+Z}{40}\leq 10

\dfrac{3X+4Y+6Z}{40}\leq 6

\dfrac{4X+6Y+5Z}{40}\leq 8

\dfrac{2X+2Y+Z}{35}+\dfrac{3X+4Y+6Z}{35}+\dfrac{4X+6Y+5Z}{35}\leq 19

4 0
2 years ago
Southern Rim Parts estimates its manufacturing overhead to be $495,000 and its direct labor costs to be $900,000 for year 1. The
Zarrin [17]

Answer:

Job 301    $   11,000

Job 302   $  16,500

Job 303   $ 22,000

Explanation:

\frac{Cost\: Of \:Manufacturing \:Overhead}{Cost \:Driver}= Overhead \:Rate

To calculate the overhead rate <u>we divide the estimated overhead cost by the estimated cost driver:</u>

\frac{495,000}{900,000}= Overhead \:Rate

0.55 overhead rate

Job 301 $20,000 labor cost x 0.55 overhead rate

11,000

Job 302 $30,000 labor cost x 0.55 overhead rate

16,500

Job 303 $40,000 labor cost x 0.55 overhead rate

22,000

8 0
2 years ago
(a. how much will accumulate in an account with an initial deposit of $100, and which earns 10% interest compounded quarterly fo
Eva8 [605]
Your answer will be B. $133.10
5 0
1 year ago
First National Bank charges 13.1 percent compounded monthly on its business loans. First United Bank charges 13.4 percent compou
FinnZ [79.3K]

Answer:

EAR for First national Bank =  13.92 %

EAR for First United Bank = 13.85 %

Explanation:

given data

First National Bank charges =  13.1 percent

compounded monthly , 1 year = 12 month

First United Bank charges = 13.4 percent

compounded semiannually , 1 year = 2 semiannually

solution

we get here first EAR for First national Bank that is express as

EAR for First national Bank = (1+ \frac{r}{n} )^n - 1 .....................1

here r is rate and n is month

so put here value

EAR for First national Bank =  (1+ \frac{0.131}{12} )^{12} - 1

EAR for First national Bank =  13.92 %

and

EAR for First United Bank   is

EAR for First United Bank = (1+ \frac{r}{n} )^n - 1   ..................2

here r is rate and n is semi annually

EAR for First United Bank = (1+ \frac{0.134}{2} )^2 - 1

EAR for First United Bank = 13.85 %

here First United bank EAR is less

5 0
1 year ago
Typhanie, a customer service representative with WestComm Wireless Services, was asked by one of her customers if WestComm would
creativ13 [48]

Answer:

E. centralized authority.

Explanation:

Centralized authority is a type of structure in which  organizational management structure where most of the major decision-making power and authority rests in the hands of a concentrated group of leaders.

8 0
1 year ago
Read 2 more answers
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