Linear Programming Model & Graphing

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Loganblahtimes2

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"A company makes two kinds of pizza: Basic and Supreme. Basic contains cheese and beef, while supreme contains cheese, onions and beef. The company sell at least 3 units a day of basic and at least 2 units of supreme. The beef costs $5 per unit for basic and $4 per unit for supreme. They can spend no more than $50 per day on beef. Dough for basic is $2 per unit while dough for supreme $1 per unit. The company can spend no more than $16 per day on dough. How many units of each kind of pizza should the company make in order to maximize profits if basic sells for $20 per unit and supreme for $15 per unit? Write a linear programming model for this company. Solve using the graphical (corner point method). Make certain to show the region of feasible solutions and each corner and step towards your final answer."

I'm very confused on this problem. I believe this would start with a system of equations. I'm sorry to say I don't have a place where I got stuck, but I honestly have no idea where to start.

Apologies for the spam recently,
I know this site says to keep your posts to a minimum, however I've been having trouble understanding a lengthy assignment. This is the last problem I've been having issues with. Thank you all for your assistance and patience.
 
basic pizza (cheese, dough and beef)
sell at least 3 units per day
beef cost $5 per unit
dough costs $2 per unit
sells for $20 per unit

supreme pizza (cheese, onions and beef
sell at least 2 units per day
beef costs $4 per unit
dough costs $1 per unit
sells for $15 per unit

can not spend more than $50 on beef
can not spend more than $16 on dough.

What are the unknowns? What is the profit equation? Can you write down the constraints?

Out of curiosity why does the basic pizza sell for more than the supreme pizza? I think that maybe you copied things wrong but it does not matter what we call the pies.
 
Answering your cu
Jomo said:
basic pizza (cheese, dough and beef)
sell at least 3 units per day
beef cost $5 per unit
dough costs $2 per unit
sells for $20 per unit

supreme pizza (cheese, onions and beef
sell at least 2 units per day
beef costs $4 per unit
dough costs $1 per unit
sells for $15 per unit

can not spend more than $50 on beef
can not spend more than $16 on dough.

What are the unknowns? What is the profit equation? Can you write down the constraints?

Out of curiosity why does the basic pizza sell for more than the supreme pizza? I think that maybe you copied things wrong but it does not matter what we call the pies.
Click to expand...

Answering your curiosity question first, I copied things right. The basic does indeed go for more than the supreme. Weird.
We have a tutorial on a problem similar to this one earlier in the course, however this problem contains many more numbers. Following that tutorial, I picked the following:
x = basic pizzas
y = supreme pizzas

Profit=20x+15y

5x+4y<=50
4x+1y<=16

Would onions be irrelevant?
 
What does x = basic pizza mean? What does y = supreme pizza mean? Define your variables.
 
Profit is NOT what you sell the item for! Profit is what you have after you sell the item and pay for all your costs. I am sure that you know that. Slow down and think a few moments and you'll get it.
 
Sorry for my misunderstanding today, I'm mentally exhausted from other problems as well.
X is the object in question coming from the basic pizza. In my costs equation for beef, I wrote 5x+4y<=50. This means that it is $5 of beef on the basic pizza, and $4 of beef on the supreme pizza. 5(basic)+4(supreme)<=$50. Beef costs from both of the pizzas cannot go over 50.

Rethinking the profit equation:
Profit on basic pizzas: $20-$5(beef)-$2(dough)=$13
Supreme: $15-$4(beef)-$1(dough)=$10
Profit=13x+10y
 
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