Using integration find the area of the triangular region whose sides have equations y=2x+1, y=3x+1 and x=4.
Equations of the lines are y = 2 x + 1, y = 3 x + 1 and x = 4.
Let y1 = 2 x + 1, y2 = 3 x + 1
Now area of the triangle bounded by the given lines,
= 8 sq. units
Thus, the area of the required triangular region is 8 square units
A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ` 100 and that on a bracelet is ` 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.
Solve the following L.P.P. graphically :
Minimise Z = 5x + 10y
Subject to x + 2y ≤ 120
Constraints x + y ≥ 60
x – 2y ≥ 0
and x, y ≥ 0
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