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jok3333 [9.3K]
3 years ago
13

Henry worked for 8 days, Jack worked for 9.5 days while Steffi worked for 6.5 days to complete a project. If the amount earned f

or the project completion was shared among them in the ratio of the number of days each one had worked, find the ratio in which the amount was shared.
Mathematics
1 answer:
trasher [3.6K]3 years ago
5 0

Answer:

The ratio in which the amount is shared is 16:19:13

Step-by-step explanation:

The given parameters are;

The number of days Henry worked = 8 days

The number of days Jack worked = 9.5 days

The number of days Steffi worked = 6.5 days

The sharing formula for the amount earned for the project = The ratio of the number of days worked by each one

The total number of days worked by all three = 8 days + 9.5 days + 6.5 days = 24 days

The fraction of the total number of days Henry worked = (8 days)/(24 days) = 1/3 = 16/48

The fraction of the total number of days Jack worked = (9.5 days)/(24 days) = 19/48

The fraction of the total number of days Steffi worked = (6.5 days)/(24 days) = 13/48

Therefore. the ratio in which the amount is shared = 16:19:13 (which is the same as the ratio of the number of days worked)

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This is a linear programming problem. In order to solve it we need to determine how we are going to use the provided data and we need to keep in mind what we need to maximize (or minimize depending on the problem)

So, the problem states that "The goal of Fine Coffees, Inc. Is to maximize profits." This last sentence will tell us what the objective function will be. The objective function must model the desired value we want to maximize. So the objective function should represent the profits of selling the two tipes of cofee blends.

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"He can only get 300 pounts of Colombian beans per week and 200 pounts of Dominican beans per week." This part or the problem is talking about the amount of coffee beans he can get depending on its type. This will help us find the restrictions for our linear programming problem, so they are not necessary to state the objective function. Next it states:

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We set A to be the number of pounds of American blend and B to be the number of pounds of British blend. So the profit for American blend is found by using the following equation:

P_{American}=$2.00*A

And the profit for the British blend is found by using the following equation:

P_{British}=$1.00*B

so the total profit is found by adding the two given profits, so we get:

P_{total}=P_{American}+P_{British}

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P_{total}=$2.00A+$1.00B

which can be simplified to:

P=2A+B

which is our objective function.

6 0
3 years ago
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