1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tresset_1 [31]
3 years ago
12

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

chines available, 6 type 2 machines available, and 8 type 3 machines available. Products 1, 2, and 3 contribute $90, $120, and $150, respectively, in marginal profit per unit produced.

Business
1 answer:
Mrac [35]3 years ago
4 0

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

You might be interested in
A woman buys a house for a ​$320000. She pays ​$40000 down and takes out a mortgage at 5.7​% for 20 years on the balance. Find h
sdas [7]

Answer:

PMT= 1957.850

Explanation:

For this case the total payment is $320000, and she pays $40000 so the remain amount to pay would be:

$320000-40000=$ 280000

For this case we assume that the annual interest rate is APR=5.7% =0.057 on fraction.

The total number of years are 20. For this case n represent the number of payments per year and since we have monthly payments then n =12.

In order to find the PMT we can use the following formula:

PMT= \frac{P(\frac{APR}{n})}{[1-(1+\frac{APR}{n})^{-nt}]}

On the last expression the APR needs to be on fraction and P represent the principal amount, for this case P = $280000. So if we replace we got:

PMT= \frac{280000(\frac{0.057}{12})}{[1-(1+\frac{0.057}{12})^{-12*20}]}

PMT= 1957.850

And we can verify this using the following excel function: "=PMT(0.057/12,12*20,-280000)"

3 0
3 years ago
Suppose you are a monopolist who faces a domestic demand curve given by Q = 1,000 –3P. Your domestic cost of production involves
Anuta_ua [19.1K]

Answer:399.17 ; 407.42

Explanation:

Given ;

Domestic cost per unit = 300

Foreign cost per unit = 150

Real exchange rate = 1.1

As a monopolist, aim is to maximize income:

Q = 1000 - 3P

THEREFORE,

Price (P) × quantity(Q) - domestic - foreign × exchange rate

P × Q - 300Q - 150Q × 1.1

P × Q - 300(1000-3P) - 150(1000-3P)×1.1

P× (1000-3P) - (300+(150×1.1))(1000-3P)

P× (1000-3P) - (465)(1000-3P)

(P-465) × (1000-3P)

1000P - 3P^2 - 465000 + 1395P

-3P^2 + 2395P-465000

P = 399.17

If real exchange rate increases by 10%,

10% of 1.1 = 0.1 × 1.1 = 0.11

0.11 + 1.1 = 1.21

simply change 1.1 to 1.21 in above equation

P× (1000-3P) - (300+(150×1.21))(1000-3P)

P× (1000-3P) - (481.5)(1000-3P)

(P-481.5) × (1000-3P)

1000P - 3P^2 - 481500 + 1444.5P

-3P^2 + 2444.5P-481500

P = 407.42

6 0
3 years ago
During inflationary periods, assets such as TIPS, gold, and real estate are used as _____________ hedges. Money demand will decr
noname [10]

Answer:

Inflation; decrease.

Explanation:

An inflation can be defined as the sustained or persistent rise in the prices of goods and services at a specific period of time. Also, an inflation hedge refers to the investment that are used to protect the eroding purchasing power of a currency (money) as a result of a persistent increase in price level due to inflation.

During inflationary periods, assets such as TIPS, gold, and real estate are used as inflation hedges.

Additionally, money demand will decrease when interest rates, payment technology, inflation risk, and the liquidity of other assets decrease. This simply means that, the desired holding of financial assets in the form of money (monetary value) is dependent on factors such as interest rates, inflation risk, payment technology etc.

5 0
3 years ago
King Electronics, a retailer of video equipment, sold two VCR's to Larson, a psychologist, for her personal use in her home. The
scoundrel [369]

Answer:

Mill's lien will prevail.

Explanation:

Generally speaking, King's security interest prevails over other the interests of unsecured creditors including credit card companies, etc. Bu tin this case, Mills had obtained a lien that was registered prior to King's security interest, therefore, a court would decide based on chronological order.

4 0
3 years ago
How does an error that results in an overstatement of ending inventory affect the elements of the company's financial statements
Kruka [31]

Answer:

A. + NA + NA - + NA

Explanation:

Since in the question there is an overstatement of ending inventory which affect the financial statements i.e increase in the gross profit due to which the net income is also increase that reflects the increment in the retained earning and the equity as well plus the asset side is also increased but it does not have any change in the cash flow statement as it does not involve any transaction of cash

Hence, the first option is correct

7 0
3 years ago
Other questions:
  • Drag the tiles to the correct boxes to complete the pairs.
    14·1 answer
  • The more illiquid something is the easier it is to turn into cash.<br><br> true or false?
    5·1 answer
  • A production department's output for the most recent month consisted of 12,500 units completed and transferred to the next stage
    14·1 answer
  • The City of West Hutchison is constructing a new road, which it estimates will cost $7.2 million. The city will finance the road
    14·1 answer
  • What are the qualities of a free-enterprise system? Check all that apply.
    10·1 answer
  • In a supermarket, a vendor's restocking the shelves every Monday morning is an example of:________
    12·1 answer
  • The following data has been provided for a compan most recent year of operations:
    11·1 answer
  • The _____ adds up the market prices of final goods and services.
    5·1 answer
  • A good measure of average should be:
    11·1 answer
  • The economic system of the united states is considered a:.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!