A factory makes tennis rackets and cricket ba | vedclass

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Question

(A) Let the number of tennis rackets be $x$ and the number of cricket bats be $y$.The machine time constraint is $1.5x + 3y \leq 42$.The craftsman's t

Vedclass · Accepted Answer

$x=4, y=12$

Vedclass · Answer

(A) Let the number of tennis rackets be $x$ and the number of cricket bats be $y$.The machine time constraint is $1.5x + 3y \leq 42$.The craftsman's time constraint is $3x + y \leq 24$.Since the factory works at full capacity, we equate these to the maximum available time:$1.5x + 3y = 42$ --- $(1)$$3x + y = 24$ --- $(2)$From equation $(2)$, we get $y = 24 - 3x$.Substitute this into equation $(1)$:$1.5x + 3(24 - 3x) = 42$$1.5x + 72 - 9x = 42$$-7.5x = 42 - 72$$-7.5x = -30$$x = \frac{30}{7.5} = 4$Now, substitute $x = 4$ into $y = 24 - 3x$:$y = 24 - 3(4) = 24 - 12 = 12$.Therefore, the factory must make $4$ tennis rackets and $12$ cricket bats.

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