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A sporting goods manufacturer allocates at least $2,400$ units of production time per day to make baseballs and footballs. It takes 20 units of time to make a baseball and 30 units of time to make a football. If $x$ represents the number of baseballs made and $y$ represents the number of footballs made, the graph of $20 x+30 y \geq 2,400$ shows the possible ways to schedule the production time. Graph the inequality. Then find three possible combinations of production time for the company to make baseballs and footballs.
(50,50),(60,50) and (50,60)
Algebra
Chapter 3
Graphing Linear Equations and Inequalities in Two Variables; Functions
Section 7
Graphing Linear Inequalities
Graphs and Statistics
Equations and Inequalities
Linear Functions
Systems of Equations and Inequalities
Missouri State University
Oregon State University
McMaster University
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So here's the equation where X represents baseballs. And what is the other one represent? Ah, footballs. Okay, so, um, we to stay under a certain number of minutes. So each access represents the number of baseballs in the number of football's we could make. All right, So let's figure out the X intercept 20 ax equals 2400 viable sides by 20 and we get 120 so we could do 120 Baseball's If we do know footballs. What about the Y intercept? 30 y equals 2400. Divide both sides by 30 and we get 80. In other words, we could do 80 um, footballs, if we do know baseballs, Um, and we do any combination there between as well, All right. And we have to do more than 2400. Okay, Yeah. 24 units of production per day. So we have to do more than that. There we go. So anything above or equal to that line. All right, so we already set a couple of combinations by three possible combinations. We could do 120 baseballs. Uh, with zero footballs, we could dio, um, 80 No. Zero baseballs with 80 footballs. And then we could do any of their point in here. So how about, uh, 90 and 70? Let's go. That so 90 baseballs and 70 football's those air different combinations that would work for us.
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