Gibson’s Gym is a fitness and aerobic center located in Austin,TX. With over 25,000 square feet of space, Gibson’s offers itscustomers an unparalleled fitness experience, including the finestequipment for cardiovascular training, resistance training, andfree-weight training. Gibson’s also features state-of-the-artaerobics, spinning, yoga, and tai chi classes taught by nationallycertified instructors. And, when not working out, patrons can enjoyother amenities such as Gibson’s tanning salon, hot tub, sauna, andjuice bar. The owners of Gibson’s Gym currently are working ontheir operating plan for the coming year, and they have providedyou with the following average membership and cost data for theprevious year:

Annual membership fee $500 per member Number of members 5,000Variable cost (supplies, instructors, etc.) $200 per member Fixedcosts (equipment, salaries, etc.) $1,200,000 The owners anticipatethat, for the coming year, both total fixed costs and the variablecost per member will remain unchanged from the previous year.

-- In addition to lowering the regular membership fee by 10%,the owners are considering offering an additional type ofmembership. Customers under the current membership plan are limitedto a certain set number of classes, services, etc. Market researchindicates that some potential members may be willing to pay morefor unlimited access to all gym amenities. To add this option, theowners would need to hire a director of premium membership, at anannual salary of $70,000 per year. The premium annual membershipfee would be $1000, and the annual cost per premium member will be$300 more than the regular member cost. Preliminary market researchsuggests 10% of members would be interested in this upgrade. Howmany premium and regular memberships must be sold in order to meeta desired after-tax profit of $315,000 (still assuming 30% taxrate, and assuming regular membership fee will be reduced by 10%from prior year)?

--The owner’s believe premium membership sales are low due tolack of awareness. They also are not currently seeing as many totalsales as they need to meet their desired level of income. They metwith an advertising firm and now believe an aggressive advertisingcampaign could boost premium membership sales up to 15% of overallsales, and that the maximum total sales they can expect to see forthe year will be 6,250 members. What is the maximum amount that theowners should pay for the advertising campaign to hit the expectedprofit $315000? What is the maximum the owners should spend on thisadvertising campaign if they want to meet a desired after-taxtarget profit of $315,000 (still assuming 30% tax rate, andassuming regular membership fee will be reduced by 10% from prioryear)?