Story problem . . . how many desks can be made?

Question

A desk company makes three different models of desks.

The lowest quality desk requires 3 hours to cut the wood, 2 hours to stain, 3 hours to assemble.

 

The middle quality desk requires 3 hours to cut the wood, 3 hours to stain, 4 hours to assemble.

 

The highest quality desk requires 4 hours to cut the wood, 4 hours to stain, 4 hours to assemble.

 

The company has 120 hours available to cut the wood, 110 hours available to stain the wood, and 130 hours available to assemble each day. How many of each type of desks can be made each day?

Answer 1

For this problem we are looking for the greatest number of each type of desk that can be cut painted and assembled. For the lowest quality desk we get the following:

120/3 = 40 which is the number of desks that can be cut.

110/2 = 55 which is the number of desks that can be stained.

130/3 = 43.333 which is the number of desks that can be assembled. We need to round that down to 43 becuase completing a third of a desk does us no good.

So if only 40 desks can be cut only 40 can be stained and only 40 can be assembled and completed.

40 of the lowest quality desks can be completed in 1 day.

We follow the same steps for the other two types.

120/3 = 40

110/3 = 36.666 = 36

130/4 = 32.5 = 32

While 40 desks can be cut, only 36 can be stained and only 32 can be assembled and completed.

120/4 = 30

110/4 = 27.5 = 27

130/4 = 32.5

While 30 of the higest quality desks can be cut, only 27 can be stained. If only 27 are stained only 27 can be assembled and completed.