The constrains for the problem are:
[tex]x+2y < =100[/tex]
[tex]\frac{7x}{4} +3y < =400[/tex]
[tex]x > =0\\y > =0[/tex]
What are constraints?
Constraints are logical conditions that a solution to an optimization problem must satisfy. They reflect real-world limits on production capacity, market demand, available funds, and so on. To define a constraint, you first compute the value of interest using the decision variables.
According to question, a catering business offers two sizes of baked ziti. Its small ziti dish uses 1 cup of sauce and [tex]1\frac{3}{4}[/tex] cups of cheese. Its large ziti dish uses 2 cups of sauce and 3 cups of cheese.
The business has 100 cups of sauce and 400 cups of cheese on hand. It makes $6 profit on their small dishes and $5 profit on their large dishes.
It wants to maximize the profit from selling the two sizes of ziti.
[tex]x[/tex] represent the number of small dishes
[tex]y[/tex] represent the number of large dishes.
So, according to question, we will get following constrains:
Business has 100 cups of sauce
⇒[tex]x+2y < =100[/tex]
Business has 400 cups of cheese
⇒[tex]\frac{7x}{4} +3y < =400[/tex]
Other constrains will small and large dishes cannot be zero.
[tex]x > =0\\y > =0[/tex]
Hence we get the following constrains:
[tex]x+2y < =100[/tex]
[tex]\frac{7x}{4} +3y < =400[/tex]
[tex]x > =0\\y > =0[/tex]
Learn more about constrains here:
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