A factory produces two products: Widgets and Sprockets. Each widget requires 2 m

Question

A factory produces two products: Widgets and Sprockets. Each widget requires 2 machine shop hours and 3 assembly line hours to produce. Each sprocket requires 0.5 machine shop hours and 0.5 assembly line hours to produce. In a given day, the factory has 52 machine shop hours and 76 assembly line hours available. If the factory would like to use all of the machine shop and assembly line hours available to it, how many of each type of product should it produce in a given day? You may use the rref calculator function to solve this problem. 36 widgets and 32 sprockets. 20 widgets and 16 sprockets. 44 widgets and 4 sprockets. 24 widgets and 8 sprockets. 48 widgets and 20 sprockets.

Explanation / Answer

Here, the answer is 24 widest and 8 sprockets. As for building 24 widest we use 24*2=48 machine shop hours, 4 machine hours left which is used to build 8 sprockets. Similarly as widget takes 3 assembly line hours so 24 widget will take 24*3 =72 i.e left over 4 is used to build 8 sprockets.

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