Camp Rainbow offers overnight summer camp programs for children ages $1014$ 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 Number of Campers Cost to Run Camp

$1140$ $$11,460$

$2908,660$

$317414,270$

$415412,090$

$517814,370$

$613211,930$

$717214,150$

$819013,590$

Required:

$4.$ Using the high$-$low method, calculate Camp Rainbow$$s total fixed operating costs and variable operating cost per child.

$5.$ Using the high$-$low method results, calculate the camp$$s expected operating cost if $172$ children attend a session.