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The minimum value of Z= 4x+5y subject to...

The minimum value of Z= 4x+5y subject to the constraints ` x le 30, yle 40 ` and ` x ge 0,y ge 0` is

A

320

B

200

C

120

D

0

Text Solution

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The correct Answer is:
D
The equalites are x = 30, y =40
The feasible region is shown in

O (O, O), A (30, 0),8(30, 40) and C (0, 40) are comer points ofOAB
` therefore ` Z at O (0, O) = 4{0) + 5(0) = O Z at A (30, 0) = 4{30} + 5(0) = 120 Zat B (0, 40) = 4{0) + 5(40) = 200 z at P (30, 40) = 4{30} + 5(40) = 320
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