Determining daily production rate and maximum profit
Corporation A produces two types of products, product X and product Y. Three machines are required to produce each type, namely, MC1, MC2, and MC3. Each product X requires 5 hours in MC1, 3 hours in MC2 and 2 hours in MC3. On the other hand, product Y requires 4 hours in MC1, 2 hours in MC2 and 3 hours in MC3. Each day there are 24 hours available for each machines. The variable cost in producing product X is $150 per unit and $120 per unit for product Y. The selling price of product X is $450 per unit and $400 per unit for product Y. The company fixed cost is $30 000. Please help me determin The daily production rate and maximum profit.
calculus optimization
edited Jan 4 at 1:45
William Elliot
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asked Jan 4 at 0:48
Carmen Mendoza
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Corporation A produces two types of products, product X and product Y. Three machines are required to produce each type, namely, MC1, MC2, and MC3. Each product X requires 5 hours in MC1, 3 hours in MC2 and 2 hours in MC3. On the other hand, product Y requires 4 hours in MC1, 2 hours in MC2 and 3 hours in MC3. Each day there are 24 hours available for each machines. The variable cost in producing product X is $150 per unit and $120 per unit for product Y. The selling price of product X is $450 per unit and $400 per unit for product Y. The company fixed cost is $30 000. Please help me determin The daily production rate and maximum profit.
calculus optimization
edited Jan 4 at 1:45
William Elliot
7,3612720
asked Jan 4 at 0:48
Carmen Mendoza
1
New contributor
Carmen Mendoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Welcome to stackexchange. You are more likely to get help rather than downvotes and votes to close if you edit the question to show us what you tried and where you are stuck. While you are doing that please fix the formatting.
– Ethan Bolker
Jan 4 at 0:51
add a comment |
Corporation A produces two types of products, product X and product Y. Three machines are required to produce each type, namely, MC1, MC2, and MC3. Each product X requires 5 hours in MC1, 3 hours in MC2 and 2 hours in MC3. On the other hand, product Y requires 4 hours in MC1, 2 hours in MC2 and 3 hours in MC3. Each day there are 24 hours available for each machines. The variable cost in producing product X is $150 per unit and $120 per unit for product Y. The selling price of product X is $450 per unit and $400 per unit for product Y. The company fixed cost is $30 000. Please help me determin The daily production rate and maximum profit.
calculus optimization
edited Jan 4 at 1:45
William Elliot
7,3612720
asked Jan 4 at 0:48
Carmen Mendoza
1
New contributor
Carmen Mendoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Corporation A produces two types of products, product X and product Y. Three machines are required to produce each type, namely, MC1, MC2, and MC3. Each product X requires 5 hours in MC1, 3 hours in MC2 and 2 hours in MC3. On the other hand, product Y requires 4 hours in MC1, 2 hours in MC2 and 3 hours in MC3. Each day there are 24 hours available for each machines. The variable cost in producing product X is $150 per unit and $120 per unit for product Y. The selling price of product X is $450 per unit and $400 per unit for product Y. The company fixed cost is $30 000. Please help me determin The daily production rate and maximum profit.
calculus optimization
calculus optimization
edited Jan 4 at 1:45
William Elliot
7,3612720
asked Jan 4 at 0:48
Carmen Mendoza
1
New contributor
Carmen Mendoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 4 at 1:45
William Elliot
7,3612720
asked Jan 4 at 0:48
Carmen Mendoza
1
New contributor
Carmen Mendoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited Jan 4 at 1:45
William Elliot
7,3612720
edited Jan 4 at 1:45
William Elliot
7,3612720
edited Jan 4 at 1:45
William Elliot
7,3612720
7,3612720
asked Jan 4 at 0:48
Carmen Mendoza
1
New contributor
Carmen Mendoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 0:48
Carmen Mendoza
1
asked Jan 4 at 0:48
Carmen Mendoza
1
1
New contributor
Carmen Mendoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Carmen Mendoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Carmen Mendoza is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
Welcome to stackexchange. You are more likely to get help rather than downvotes and votes to close if you edit the question to show us what you tried and where you are stuck. While you are doing that please fix the formatting.
– Ethan Bolker
Jan 4 at 0:51
add a comment |
1
Welcome to stackexchange. You are more likely to get help rather than downvotes and votes to close if you edit the question to show us what you tried and where you are stuck. While you are doing that please fix the formatting.
– Ethan Bolker
Jan 4 at 0:51
1
1
Welcome to stackexchange. You are more likely to get help rather than downvotes and votes to close if you edit the question to show us what you tried and where you are stuck. While you are doing that please fix the formatting.
– Ethan Bolker
Jan 4 at 0:51
Welcome to stackexchange. You are more likely to get help rather than downvotes and votes to close if you edit the question to show us what you tried and where you are stuck. While you are doing that please fix the formatting.
– Ethan Bolker
Jan 4 at 0:51
add a comment |
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In general for a problem like this you want to use the Simplex method. But this problem is small enough that you can solve it by just checking a few cases.
Product X takes $5$ hours on MC1 so you can make at most $4$ of X each day. Given that you want to make as many products as possible, the optimal choice will be one of the following (X,Y) tuples:(4,1),(3,2),(2,3),(1,4),(0,6). X gives you a profit of $300$ and Y a profit of $280$ so the profits for the above choices are $1480$, $1460$, $1440$, $1420$, and $1680$, respectively. So the optimal choice is to produce 6 of Y and 0 of X, for a daily profit of $1680$.
answered Jan 4 at 6:44
Erik Parkinson
9159
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In general for a problem like this you want to use the Simplex method. But this problem is small enough that you can solve it by just checking a few cases.
Product X takes $5$ hours on MC1 so you can make at most $4$ of X each day. Given that you want to make as many products as possible, the optimal choice will be one of the following (X,Y) tuples:(4,1),(3,2),(2,3),(1,4),(0,6). X gives you a profit of $300$ and Y a profit of $280$ so the profits for the above choices are $1480$, $1460$, $1440$, $1420$, and $1680$, respectively. So the optimal choice is to produce 6 of Y and 0 of X, for a daily profit of $1680$.
answered Jan 4 at 6:44
Erik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
In general for a problem like this you want to use the Simplex method. But this problem is small enough that you can solve it by just checking a few cases.
Product X takes $5$ hours on MC1 so you can make at most $4$ of X each day. Given that you want to make as many products as possible, the optimal choice will be one of the following (X,Y) tuples:(4,1),(3,2),(2,3),(1,4),(0,6). X gives you a profit of $300$ and Y a profit of $280$ so the profits for the above choices are $1480$, $1460$, $1440$, $1420$, and $1680$, respectively. So the optimal choice is to produce 6 of Y and 0 of X, for a daily profit of $1680$.
answered Jan 4 at 6:44
Erik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
In general for a problem like this you want to use the Simplex method. But this problem is small enough that you can solve it by just checking a few cases.
Product X takes $5$ hours on MC1 so you can make at most $4$ of X each day. Given that you want to make as many products as possible, the optimal choice will be one of the following (X,Y) tuples:(4,1),(3,2),(2,3),(1,4),(0,6). X gives you a profit of $300$ and Y a profit of $280$ so the profits for the above choices are $1480$, $1460$, $1440$, $1420$, and $1680$, respectively. So the optimal choice is to produce 6 of Y and 0 of X, for a daily profit of $1680$.
answered Jan 4 at 6:44
Erik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
In general for a problem like this you want to use the Simplex method. But this problem is small enough that you can solve it by just checking a few cases.
Product X takes $5$ hours on MC1 so you can make at most $4$ of X each day. Given that you want to make as many products as possible, the optimal choice will be one of the following (X,Y) tuples:(4,1),(3,2),(2,3),(1,4),(0,6). X gives you a profit of $300$ and Y a profit of $280$ so the profits for the above choices are $1480$, $1460$, $1440$, $1420$, and $1680$, respectively. So the optimal choice is to produce 6 of Y and 0 of X, for a daily profit of $1680$.
answered Jan 4 at 6:44
Erik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Jan 4 at 6:44
Erik Parkinson
9159
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Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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answered Jan 4 at 6:44
Erik Parkinson
9159
answered Jan 4 at 6:44
Erik Parkinson
9159
9159
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New contributor
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Welcome to stackexchange. You are more likely to get help rather than downvotes and votes to close if you edit the question to show us what you tried and where you are stuck. While you are doing that please fix the formatting.
– Ethan Bolker
Jan 4 at 0:51