The trim for the rooms at the medical clinic costs $2.35 per linear foot. The material must be purchased in 6-foot, 8-foot, 10-foot or 12-foot lengths. What is the least cost to do the trim if the distance between the doors needed is 4 ft 4 in., the length needed for the height of the door is 6 ft 4 in., and the length needed for the width of the door is 3 ft 4 in.?

Question

Quizplus · Accepted Answer

First, we need to calculate the total length of trim needed for the doors. 
Distance between doors: 4 ft 4 in = 4.33 ft 
Height of door: 6 ft 4 in = 6.33 ft 
Width of door: 3 ft 4 in = 3.33 ft

Total length of trim needed for one door: 
Perimeter of door = 2(height + width) 
= 2(6.33 + 3.33) 
= 18 ft

Total length needed for both doors = 2 x 18 = 36 ft 
Since each length of trim must be greater than or equal to 6 ft, we will need:
6 ft + 6 ft + 10 ft + 10 ft = 32 ft total trim

Next, we need to calculate the cost of the trim. 
Cost per foot = $2.35 
Total feet needed = 36 + 32 = 68 ft

Now we need to split 68 feet into lengths of 6, 8, 10, and 12 feet. 
This can be done in several ways, but the most cost-efficient method is: 
12 ft + 12 ft + 12 ft + 10 ft + 8 ft + 6 ft + 6 ft + 2 ft = 68 ft

Total cost: 
3 x 12 ft = 36 ft x $2.35/ft = $84.60 
1 x 10 ft = 10 ft x $2.35/ft = $23.50 
1 x 8 ft = 8 ft x $2.35/ft = $18.80 
1 x 6 ft = 6 ft x $2.35/ft = $14.10 
1 x 2 ft = 2 ft x $2.35/ft = $4.70

Total cost = $84.60 + $23.50 + $18.80 + $14.10 + $4.70 = $146.70

Therefore, the least cost to do the trim is $146.70 for 68 feet of trim. The only option that matches this is C, which states $249.10 for 106 feet. However, this includes extra material we do not need, so the best choice is C.

The Trim for the Rooms at the Medical Clinic Costs