A dairy company can make 1200 units of product each week. To meet the needs of its regular customers,
the dairy company must produce 300 units of cheese, and 450 units of yogurt. If the profit for each unit of
cheese is $60 and for each unit of yogurt is $90, how many units of each type of dairy product should the
dairy company make to maximize its profit?
300 yogurt and 450 cheese

Explanation:

1. Name the variables:

2. State the constraints (inequalities)

a) Company can make 1,200 units of product each week:

b) Company must produce at least 300 units of cheese,

c) Company must produce at least 450 units of yogurt.

3. Build the graph

a) C + Y ≤ 1,200

i) Draw the line C + Y = 1,200

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.

4. Determine the vertices of the triangle that forms the solution region

a) Intersection of the lines C + Y = 1,200 and C = 300

b) Intersection of the lines C + Y = 1200 and Y = 450

c) Intersection fo the lines C = 300 and Y = 450

5. Determine the profits with the three vertices

The profit equation is P = $60C + $90Y

a) Point (300, 900)

b) Point (750, 450)

c) Point (300, 450)

The maximum profit is when the company produces 300 units of cheese and 900 units of yogurt.

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step-by-step explanation: