Boat Sales. Dry Boat Works wholesales aluminum boats for 800...

Boat Sales. Dry Boat Works wholesales aluminum boats for $$ 800$ and fiberglass boats for $ 600 .$ Northland Marina wants to order at least $2,400$ worth but no more than $4,800$ worth of boats from them. Use the illustration to graph a system of inequalities that will show the possible combinations of the number of aluminum boats $(x)$ and the number of fiberglass boats ( $y$ ) that can be ordered. Give two possible solutions. (GRAPH CANNOT COPY)

Key Concepts

System of Inequalities

This concept involves representing multiple constraints using inequalities that must be satisfied simultaneously. In practical problems, each inequality restricts the values that the decision variables can take based on conditions such as cost, quantity, or resource limits.

Linear Model

A linear model expresses a relationship between variables with linear equations or inequalities. It translates a real-world scenario into a mathematical form where cost and quantity, for example, are related through constant coefficients, allowing for systematic analysis and solution finding.

Graphing Linear Inequalities

This involves plotting the equations corresponding to the equality parts on a coordinate plane and then shading the region that satisfies the inequality conditions. It provides a visual representation of the constraints, making it easier to identify solutions that meet all requirements.

Feasible Region

The feasible region is the area on the graph where all the inequalities in a system overlap. It represents all the possible combinations of variables that satisfy every constraint imposed by the problem, hence identifying all viable solutions.

Transcript

00:01 Okay, so for this problem, it says, dry boatworks, wholesales, aluminum boats for $800 and fiberglass boats for $600.

00:11 So aluminum is $800 and fiberglass is $600.

00:22 Northland marina wants to order at least $2 ,400 worth but no more.

00:32 But no more than 4 ,800.

00:44 Okay.

00:46 Use the illustration to graph the system of linear equations that shows the possible combinations of the number of aluminum boats and the number of fiberglass boats that can be ordered.

00:58 Give two possible solutions.

01:00 Okay.

01:02 So we have aluminum boats is x.

01:07 And we have fiberglass boats is y so we have that it's 800 x plus 600 y is less than or equal to 4800 but greater than or equal to 4800 i mean 2 ,400 200 okay so so, if i write two equations with this, i would actually do 800x plus 600y is less than or equal to 4800.

02:04 And then 800x plus 600 y is greater than or equal to 2 ,400.

02:14 Now, what i'm going to do is i am going to put these in slope intercept form.

02:21 So i am going to have the 800x plus 600y is less than or equal to 4 ,800.

02:39 And so if i do 600, y is less than or equal to 800 plus 4800 x.

02:50 And so divide by 600.

02:52 So then i have y is less than or equal to two.

03:02 So four over three x plus get rid of those eight.

03:11 And so then if i plot this eight and that would be a negative four thirds.

03:21 Sorry, down four, one, two, three, four to the right three, down four to the right three...