E$15-22.$ Developing an Equation from Average Costs

Tucker Pup's Pet Resort offers dog boarding services in Chicago. Assume that in March, when dog$-$

days occupancy was at an annual low of $150$ days, the average cost per dog$-$day was $$65.$ In July, when

dog$-$days 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.