Answer
Verified
447.3k+ views
Hint: Let x be the number of necklaces manufactured and y be the number of bracelets manufactured. Using the condition: the total number of necklaces and bracelets that it can handle per day is at most 24, form one constraint. Using maximum number of hours form another constraint. Then using the condition that at least one of each must be produced, form two more constraints. These will be the four constraints. Next, let the profits be z. Use the condition that the profit on a necklace is Rs. 100 and that on a bracelet is Rs. 300 to form an equation which needs to be maximised. This is the L.P.P.
Complete step-by-step answer:
In this question, we are given that a small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and a half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs. 100 and that on a bracelet is Rs. 300.
We need to formulate an L.P.P. for finding how many of each should be produced daily to maximize the profit.
Let x be the number of necklaces manufactured and y be the number of bracelets manufactured. The total number of necklaces and bracelets it can handle is at most 24, so, according to the question,
$x+y\le 24$
The necklaces take $x$ hours to manufacture and bracelets take $\dfrac{y}{2}$ hours to manufacture and the maximum time available is for 16 hours. So,
\[x+\dfrac{y}{2}\le 16\]
The profit on one necklace is given as Rs. 100 and the profit on one bracelet is given as Rs. 300.
Let the profit be z. So,
$z=100x+300y$
Therefore, we need to maximize
$z=100x+300y$
Subject to the constraints
$x+y\le 24$ and
\[x+\dfrac{y}{2}\le 16\]
$x\ge 1$ and $y\ge 1$
max $z=100x+300y$ is the required L.P.P.
Note: In this question, it is very important to note that the question asks us to formulate an L.P.P. only to find how many of each should be produced daily to maximize the profit. We do not actually have to find the values of x and y or the maximum profit. Some students may not understand this and solve it to get the values which will waste their time.
Complete step-by-step answer:
In this question, we are given that a small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and a half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is Rs. 100 and that on a bracelet is Rs. 300.
We need to formulate an L.P.P. for finding how many of each should be produced daily to maximize the profit.
Let x be the number of necklaces manufactured and y be the number of bracelets manufactured. The total number of necklaces and bracelets it can handle is at most 24, so, according to the question,
$x+y\le 24$
The necklaces take $x$ hours to manufacture and bracelets take $\dfrac{y}{2}$ hours to manufacture and the maximum time available is for 16 hours. So,
\[x+\dfrac{y}{2}\le 16\]
The profit on one necklace is given as Rs. 100 and the profit on one bracelet is given as Rs. 300.
Let the profit be z. So,
$z=100x+300y$
Therefore, we need to maximize
$z=100x+300y$
Subject to the constraints
$x+y\le 24$ and
\[x+\dfrac{y}{2}\le 16\]
$x\ge 1$ and $y\ge 1$
max $z=100x+300y$ is the required L.P.P.
Note: In this question, it is very important to note that the question asks us to formulate an L.P.P. only to find how many of each should be produced daily to maximize the profit. We do not actually have to find the values of x and y or the maximum profit. Some students may not understand this and solve it to get the values which will waste their time.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Why Are Noble Gases NonReactive class 11 chemistry CBSE
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
At which age domestication of animals started A Neolithic class 11 social science CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Write a letter to the principal requesting him to grant class 10 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE