Question

Can anyone help explain how to solve this problem?

A company makes two kinds of products: Basic and Advanced. To manufacture the Basic takes 3 hours in Assembly and 2 hours in Finishing. To manufacture the Advanced takes 2.4 hours in Assembly and 2.4 hours in Finishing. The Assembly department has 2,678 hours per week and the Finishing department has 2,341 hours per week. How many of each type of product should be manufactured to run at capacity?
If necessary, round DOWN to the nearest whole number.

Answer 1

337 Basic products; 694 Advanced products

Explanation:

You want the numbers of products that should be produced to run the factory at capacity if ...

• Basic takes 3 Assembly and 2 Finishing hours
• Advanced takes 2.4 Assembly and 2.4 Finishing hours
• Capacity is 2678 Assembly and 2341 Finishing hours

Setup

You add up the assembly and finishing hours and set them to their respective capacity limits.

3b +2.4a = 2678 . . . . . . . . assembly hours

2b +2.4a = 2341 . . . . . . . . . finishing hours

Solution

Subtracting the second equation from the first gives ...

(3b +2.4a) -(2b +2.4a) = (2678) -(2341)

b = 337 . . . . . . . . . . . simplify

2(337) +2.4a = 2341

2.4a = 1667 . . . . . . . . . subtract 674

a = 694.5833... . . . . . . divide by 2.4

Rounding down gives b = 337, a = 694.

The company should manufacture 337 Basic and 694 Advanced products to run at capacity.

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Additional comment

There will be 1.4 hours left over in each department, not enough to produce another product of either kind.

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