Question

Required information Camp Rainbow offers overnight summer camp programs for children ages 10-14 every summer during June and July. Each camp session is one week and can accommodate up to 200 children. The camp is not coed, so boys attend during the odd-numbered weeks and girls attend during the even-numbered weeks. While at the camp, participants make crafts, participate in various sports, help care for the camp's resident animals, have cookouts and hayrides, and help assemble toys for local underprivileged children. The camp provides all food as well as materials for all craft classes and the toys to be assembled. One cabin can accommodate up to 10 children, and one camp counselor is assigned to each cabin. Three camp managers are on-site regardless of the number of campers enrolled. Following is the cost information for Camp Rainbow's operations last summer: Week 00 VOUW Number of Cost to Run Campers Camp 94 $8,630 140 11, 740 108 8,830 120 9,400 118 9, 010 100 8,610 90 8, 680 124 9,590

Answer 1

Week	No. of campers(X)	Camp Cost(Y)(in $)	Square of X	X*Y(in $)
1	94	8,630	8,836	8,11,220
2	140	11,740	19,600	16,43,600
3	108	8,830	11,664	9,53,640
4	120	9,400	14,400	11,28,000
5	118	9,010	13,924	10,63,180
6	100	8,610	10,000	8,61,000
7	90	8,680	8,100	7,81,200
8	124	9,590	15,376	11,89,160
Total	894	74,490	1,01,900	84,31,000
	Unit Variable Cost (b) = nΣxy − (Σx)(Σy) /nΣx^2 − (Σx)^2		Total Fixed Cost (a) = Σy − bΣx / n
So here n =8 ,Σx =894 Σy =74,490, Σx^2=101,900 ,Σxy =8,431,000
Variable cost per unit(b) =8*8,431,000 - (894*74,490) / 8*101,900 - 894^2
Variable cost per unit(b) =(67,448,000 - 66,594,060) / 815,200 - 799,236
Variable cost per unit(b) = 853,940 / 15,964 =$53.49 per unit
Total Fixed cost =74,490 - ($53.94*894) / 8
Total Fixed cost =(74,490 - 48,222) / 8
Total Fixed cost =$26,268 /8 =$3,283.46
The cost volume formula is:
y =$3,283.46 + $53.49X
Intercept	$3,283.46
X Variable 1	$53.49
Total Cost if 90 children attended the session =$3,283.46 + $53.49*90
Total Cost if 90 children attended the session =$3,283.46 + 4,814.10 =$8,097.56