Which graph represents a function with direct variation?
2 answers:
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Answer:
- <u>300 cheese and 900 yogurt</u>
Explanation:
<u>1. Name the variables: </u>
<u />
- C = number of units of cheese
- Y = number of units of yogurt
<u>2. State the constraints (inequalities)</u>
a) Company can make 1,200 units of product each week:
- C + Y ≤ 1,200
b) Company must produce at least 300 units of cheese,
- C ≥ 300
c) Company must produce at least 450 units of yogurt.
- Y ≥ 450
<u />
<u>3. Build the graph</u>
a) C + Y ≤ 1,200
i) Draw the line C + Y = 1,200
- Use the y-intercept (0, 1200) and the x-intercept (1200,0)
- Use a solid line because thepoints on the line are part of the solution
ii) Shade the region below the line (again the line is inclueded)
b) C ≥ 300
i) Draw a solid vertical line that passes through (300,0)
ii) Shade the region to the right of the line (the line is included)
c) Y ≥ 450
i) Draw a solid horizontal line that passes through (450, 0)
ii) Shade the region above the line (the line is included)
The solution region is delimited by those three lines and it is shown on the graph attached.
<u>4. Determine the vertices of the triangle that forms the solution region</u>
a) Intersection of the lines C + Y = 1,200 and C = 300
- Y = 1,200 - 300 = 900
- Point (300, 900)
b) Intersection of the lines C + Y = 1200 and Y = 450
- C = 1,200 - 450 = 750
- Point (750, 450)
c) Intersection fo the lines C = 300 and Y = 450
- Point (350, 450)
<u />
<u>5. Determine the profits with the three vertices</u>
The profit equation is P = $60C + $90Y
a) Point (300, 900)
- P = $60(300) + $90(900) = $99,000
b) Point (750, 450)
- P = $60(750) + $90(450) = $85,500
c) Point (300, 450)
- P = $60(300) + $90(450) = $58,500
The maximum profit is when the company produces 300 units of cheese and 900 units of yogurt.
