A Rancher is mixing two types of food, Brand X and Brand Y for his cattle. If each serving is required to have 60 grams of protein and 30 grams of fat, where Brand A has 15 grams of protein and 10 grams of fat and costs 80 cents per unit, and Brand B contains 20 grams of protein and 5 grams of fat, and cost 50 cents per unit, how much of each type should be used to minimize cost to the Rancher? a. Formulate a linear Programming model for this problem b. Solve this method by using Solver method
Answers
Answer:
Brand A Q 2.4
Brand B Q 1.2
Explanation:
Using Excel solver:
contrains:
c4 = 60
d4 = 30
solve e4 for min
variable cell b2:b3
a b c d e
Q Protein Fat Cost
Brand A 2.4 36 24 1.92
Brand B 1.2 24 6 0.6
60 30 2.52
Protein = 60
Fat = 30
Final answer:
Firstly, you have to formulate the objective function and constraints by using the given information. After inputting the model into a solver program, the program will provide the values that deliver the minimum value for the objective function that is subject to the constraints. This is a high school level mathematics problem.
Explanation:
In order to form a linear programming model, you would need to define your decision variables, in this case the amount of food from both brands. If we denote the amount of Brand X food by x and the Brand Y food by y, the objective function (the thing you want to minimize, the cost in this case) will be 0.8x + 0.5y. The constraints are the nutritional requirements: 15x + 20y >= 60 for protein, and 10x + 5y >= 30 for fat.
To solve this model using the Solver method, you would input your model into a solver program and find the values of x and y that minimize the objective function while adhering to the constraints. Result will depend on the specific program used.
This problem, by nature, falls under the Mathematics subject matter, as it involves linear algebra and optimization. It's likely a High School/Early College level question as it involves the application of linear programming models to practical real-world problems.
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A relatively flat demand curve indicates that the demand for a product is very sensitive to a change in price.TrueFalse
Answers
Answer:
Loss on bond redemption = $3 million
Explanation:
Given:
Face value = $15 million
Carrying value = $13 million
Cash paid = $16 million
Find:
Profit / loss
Computation:
Loss on bond redemption = Carrying value - Cash paid
Loss on bond redemption = $13 million - $16 million
Loss on bond redemption = $3 million
The entry to record the retirement will include option E. A loss of $3 million. To understand the calculation see below.
Bond Redemption
We are provided with the information about :
Face value = $15 million
Carrying value = $13 million
Cash paid = $16 million
We need to find profit or loss. The difference between Carrying value and Cash paid is the profit or loss.
Carrying Value - Cash paid
$13 million - $16 million
-$3 million, the answer is negative hence there is loss.
Therefore, the correct option is E. A loss of $3 million.
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Answers
Answer:
$378.75
Explanation:
Data provided:
Capacity = 440 passengers
Operating cost = $4,000 + $70(Number of passengers)
Expected number of passengers = 440 - 0.64T
Ticket price = T
Total operational cost = $4000 + $70( 440-0.64T )
Total operational cost = $34,800 - 44.8T
Thus,
Total revenue = Number of passengers × Ticket price
= (440 - 0.64T)T
= 440T - 0.64T²
also,
Total profit ,P(T) = Total revenue - Total operational cost
P(T) = ( 440T - 0.64T²) - (34,800 - 44.8T)
P(T) = - 0.64T² - 34,800 + 484.8T
Now,
Differentiating with respect to ticket price T
P'(T) = -0.64(2)T - 0 + 484.8(1)
or
P'(T) = - 1.28T + 484.8 ..............(1)
For point of maxima or minima
P'(T) = 0
or
- 1.28T + 484.8 = 0
or
1.28T = 484.8
or
T = $378.75
now,
again differentiating (1) to check for maxima or minima
P''(T)= -1.26(1) + 0
P''(T) = -1.26
Since,
P"(T) < 0
Hence,
T = $378.75 will maximise the profit
Final answer:
The airline's profit can be maximized with a ticket price of approximately $289.84 as calculated from the provided mathematical model. However, real-world variables may affect actual optimal pricing.
Explanation:
In this case, the airline's profit function (revenue minus costs) can be written as: P(T) = T*(440 - 0.64T) - (4000 + 70*(440 - 0.64T)). To maximize profit, you would take the derivative of P(T) with respect to T, resulting in the following polynomial: P'(T) = 440 - 1.28T - 70. Setting this derivative equal to zero and solving for T yields a ticket price of approximately $289.84.
Another way to check this solution would be to create a graph of the function P(T) and visually identify the maximum point. Mind you, this method requires precision and may not generate the accurate result as the calculus method.
It's important to keep in mind that this is a simplified model and doesn't account for other factors which can affect ticket pricing in the real world, such as competition, fuel prices, and demand for specific flights. That being said, this exercise highlights how mathematical models can be used in economics and business to optimize profit by adjusting pricing strategies.
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Answers
Answer:
The maximum amount that could be paid for the antique pitcher is $13.93 as shown by the workings in the explanation section below.
Explanation:
Since the maximum price that could be charged for the antique pitcher is $17,the most that could be paid in purchasing it, is given by the below formula:
selling price * 100% / (100% + Markup%)
=$17*100%/(100%+22%)
=$13.93
From the foregoing analysis,the markup in dollar terms is $17-$13.93=$3.07 which represents 22% of the cost price of the antique pitcher.
Answers
Answer:
The correct answer is letter "B": A personal interest.
Explanation:
Businesses based on consumers' personal interests attempt to provide a tailored good or service. The competitive advantage of the organization relies on the uniqueness of the product they can provide to their clients compared to competitors who tend to offer products with wide features to cover the larger amount of needs possible.
Conducting businesses driven by customers' personal interests requires constant studies of consumer patterns to adapt in front of market changes and segmentation to identify what sector of the market the company will dedicate their efforts to.
Answers
Answer:
A 15-year mortgage monthly payments is: $1,496.5
A 30-year mortgage monthly payments is: $1,060.1
=> The difference of monthly payment between the two options is: $436.4 ( $1,496.5 - $1,060.1) where the monthly payment of the option of 15-year mortgage is higher.
Explanation:
The borrowed amount in both options is : $250,000 * 80% = $200,000;
* A 15-year mortgage monthly payments is:
We have (1+APR) = ( 1 + Monthly Interest rate)^12 <=> 1.0425 = ( 1 + Monthly Interest rate)^12 <=> Monthly Interest rate = 0.3475%;
Amount of payment periods = 15 * 12 = 180
=> Monthly payment = (200,000 * 0.3475%) / [ 1 - 1.003475^(-180) ] = $1,496.5
* A 30-year mortgage monthly payments is:
We have (1+APR) = ( 1 + Monthly Interest rate)^12 <=> 1.05 = ( 1 + Monthly Interest rate)^12 <=> Monthly Interest rate = 0.4074%;
Amount of payment periods = 30 * 12 = 360
=> Monthly payment = (200,000 * 0.4074%) / [ 1 - 1.004074^(-360) ] = $1,060.1
Answers
Answer:
(1) Controllable margin $ 191420
(2) Variable Costs$ 371580
(3) Contribution Margin $ 146380
(4)Controllable fixed costs $45,040
(5) Controllable fixed costs $ 95710
(6) Sales $ 484,180
Explanation:
The workings have been done to show the results.
Swifty Inc.
Women’s Shoes Men’s Shoes Children’s Shoes
Sales 675,600 506,700 (6) $ 484180
Variable costs (2)$ 371580 360,320 281,500
C. Margin $304,020 $ (3)146380 $202,680
(2) Variable Costs = Sales - Contribution Margin= 675600- 304020=
$ 371580
(3) Contribution Margin= Sales - Variable Costs = 506,700-360,320 = $ 146380
(6) Sales = Contribution Margin + Variable Costs= 281,500 +$202,680 = $ 484,180
Swifty Inc.
Women’s Shoes Men’s Shoes Children’s Shoes
Sales 675,600 506,700 $ 484180
Variable costs $ 371580 360,320 281,500
C. Margin $304,020 $ 146380 $202,680
Controllable
fixed costs 112,600 (4) $45,040 (5) $ 95710
Controllable margin (1) $ 191420 101,340 106,970
(1) Controllable margin=Contribution Margin-Controllable fixed costs
= $ 304,020 -112,600 =$ 191420
(4) Contribution Margin- Controllable margin=Controllable fixed costs
$ 146380 - 101,340 = $45,040
(5) Contribution Margin- Controllable margin=Controllable fixed costs
$202,680 - 106,970 = $ 95710