For problems like this, I try to find the upper bound first. That way, I can get an idea for how efficiently I can use my materials.
11.8 inches * 5 ft =>
11.8 inches * 60 inches =>
118 * 6 square inches =>
(600 + 60 + 48) square inches =>
708 square inches
4 inches * 5 inches =>
20 square inches
708 / 20 =>
70.8 / 2 =>
35.4
So no matter what, the most pieces you could get, if things were perfect, would be 35.
Now, the best way you can lay these out would be in a grid pattern whose divisions run parallel to the sides of the paper. You can either let the 4 inch sides run parallel to the 60 inch side or you could let the 5 inch side run parallel. No matter what, you'll only be able to tile 2 pieces along the shorter side. If you laid them out with the 4 inch side parallel to the 60 inch side, you'd get 30 pieces. If you laid them out with the 5 inch side parallel to the 60 inch side, you'd get 24 pieces. There's 1 other way to lay them out, which would give you a 9 inch by 20 inch block, but you'd only get 27 pieces from that.
So the most you're going to get is 30 pieces. Lay the 5 inch side parallel to the short side of your material and the 4 inch side parallel to the long side of your material.
Either 4 inches or 5 inches goes evenly into 5 feet, but neither goes evenly into 11.8 inches (if only it was 0.2 inches wider). So which ever way you orient them, there will be some waste. To maximize the number of pieces you can get, you have to minimize the width of the wasted piece.
if you lay your pieces 4 inches across, you get two pieces totaling 8 inches, with 3.8 inches wasted. If you lay your pieces 5 inches across, you also get two pieces - totaling 10 inches, but with only 1.8 inches wasted. So the minimal width of the wasted piece is 1.8 inches.
That means you can get fifteen 4-inch rows out of 5 feet, and two 5-inch columns out of 10 inches. For thirty pieces total.
Five feet = 60 inches; 60 ÷ 4 = 15; you can make 15 strips that are 10 by 4 inches then cut them in half: 30 pieces. The extra 1.8 by 60 inch strip gets wasted.
Answers & Comments
For problems like this, I try to find the upper bound first. That way, I can get an idea for how efficiently I can use my materials.
11.8 inches * 5 ft =>
11.8 inches * 60 inches =>
118 * 6 square inches =>
(600 + 60 + 48) square inches =>
708 square inches
4 inches * 5 inches =>
20 square inches
708 / 20 =>
70.8 / 2 =>
35.4
So no matter what, the most pieces you could get, if things were perfect, would be 35.
Now, the best way you can lay these out would be in a grid pattern whose divisions run parallel to the sides of the paper. You can either let the 4 inch sides run parallel to the 60 inch side or you could let the 5 inch side run parallel. No matter what, you'll only be able to tile 2 pieces along the shorter side. If you laid them out with the 4 inch side parallel to the 60 inch side, you'd get 30 pieces. If you laid them out with the 5 inch side parallel to the 60 inch side, you'd get 24 pieces. There's 1 other way to lay them out, which would give you a 9 inch by 20 inch block, but you'd only get 27 pieces from that.
So the most you're going to get is 30 pieces. Lay the 5 inch side parallel to the short side of your material and the 4 inch side parallel to the long side of your material.
Either 4 inches or 5 inches goes evenly into 5 feet, but neither goes evenly into 11.8 inches (if only it was 0.2 inches wider). So which ever way you orient them, there will be some waste. To maximize the number of pieces you can get, you have to minimize the width of the wasted piece.
if you lay your pieces 4 inches across, you get two pieces totaling 8 inches, with 3.8 inches wasted. If you lay your pieces 5 inches across, you also get two pieces - totaling 10 inches, but with only 1.8 inches wasted. So the minimal width of the wasted piece is 1.8 inches.
That means you can get fifteen 4-inch rows out of 5 feet, and two 5-inch columns out of 10 inches. For thirty pieces total.
The wasted area is 1.8 inches by 5 feet.
Five feet = 60 inches; 60 ÷ 4 = 15; you can make 15 strips that are 10 by 4 inches then cut them in half: 30 pieces. The extra 1.8 by 60 inch strip gets wasted.