A factory produces two types of widgets: Type A and Type B. Producing

Question

A factory produces two types of widgets: Type A and Type B. Producing one Type A widget requires 3 hours of labor and 2 units of raw material, while producing one Type B widget requires 5 hours of labor and 4 units of raw material.
The factory has a maximum of 60 hours of labor and 40 units of raw material available in a week. If the factory produces only Type A and Type B widgets, what is the maximum number of widgets it can produce in a week?

A. 14
 B. 15
 C. 16
 D. 18
 E. 20

BhavikaA · Answer

got the right answer, unsure about approach.

slim626 · Answer

First time commentor, so please bear with me here.

Since the question is asking to maximize the output of widgets per week, we want to find the maximum number of widgets we can create with our labor and material budget.

Since Widget A costs less in labor and material, we can choose to only produce Widget A. At a cost of 3 labor hours and 2 material units per widget, we can exhaust the 60 labor hour and 40 material unit budget to make 20 Widget As.

Open to feedback on optimizing this approach / thinking through things less intuitively and with more structure.

Souradeep17 · Answer

You have 60 hours and 40 units of raw material 
For type A you need 3 hours and 2 units of Raw mat. 
So basically you can manufacture 20 type A widget

For type B you need 5 hours and 4 units : 
So here will be able to manufacture at most 10 as 40 raw material/4 (req by Type B);
Since type A is max between A and B we choose 20 as the answer

Amity007 · Answer

let be the no of type A and Type B is x and y resp.
so time rq. 3x+5y=60 
material rq. 2x+4y=40
by solving these x+y=20, so the answer is 20

IshmaelJN · Answer

In this question, the goal is maximize output.

This factory is capacity constrained with 60 hours of labor and 40 units of raw materials.

Note, the question does mention a minimum amount of A or B (be on the lookout for this).

Due to this, we can maximize output by only producing type A:

60 hours / 3 hours = 20 units

A factory produces two types of widgets: Type A and Type B. Producing

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A factory produces two types of widgets: Type A and Type B. Producing

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