$-25(15$ points$)$ Developing an Equation from Average Costs: Tucker Pup$$s Pet Resort offers dog

boarding services in Chicago. Assume that in March, when dog$-$day occupancy was at an annual low of

$150$ days, the average cost per dog$-$day was $$65.$ In July, when dog$-$day were at a capacity level of $600,$

the average cost per dog$-$day was $$20.$

Required

a$.$ Develop an equation for monthly operating costs.

b$.$ Determine the average boarding cost per dog$-$day at an annual volume of $4,500$ dog$-$days.