Question

Today, your carpentry shop must produce 330 chair railings where each railing is made from a single piece of fine wood. Your three step manufacturing process has the following scrap rates for the corresponding step: Step 1: 1.1% Step 2: 1.1% Step 3: 1.6% How many pieces of wood must you start with to have 330 railings that can be sold

Answer 1

Answer:

343 pieces of wood.

Step-by-step explanation:

In order to determine the starting number of pieces of wood that yield 330 railings, the easiest course of action is to work your way back through step 3, step 2, and step 1. The number of pieces that must arrive at each step are given by:

$n_f=330\\n_3 = \frac{330}{1-0.016}\\n_2 = \frac{n_3}{1-0.011}\\n_1 = \frac{n_2}{1-0.011} \\\\n_3 = 335.3658\\n_2=339.09591\\n_1=342.86745=343$

Rounding up to the next whole piece, 343 pieces are needed.

Therefore, you must start with 343 pieces of wood to have 330 railings that can be sold.