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35. The Eco-venture charter company offers local environmental excursions. The fare is $45 per person if 18-30 passengers sign up for the trip. The company does not offer the trip if fewer than 18 people sign up. If more than 30 people sign up, the fare for every passenger is reduced by $1 for each passenger in excess of 40, The bus can hold only 48 (ANS: 37 or 38) passengers. Determine the number of passengers that generates the greatest revenue for the charter company. 36. An ice cream vendor has found that the cost of supplying x cones is C(x) = 25 + 0.12x + 0.001x and also that the demand for the cones increases when the price drops. Approximately 500 cones will sell per day if they are priced at $1.20, but for every price drop of 10 cents, the number sold increases by 20. Similarly, for every price increase of 10 cents, the number sold per day decreases by 20. a) Determine the price of the cones that maximizes revenue. (ANS; $1.85) b) Determine the prices of the cones that maximizes profit. (ANS: $2.21) 37. The manager of a 240 room ski resort has found that, on average, 150 rooms are booked when the price is $175 per night and 160 rooms are booked when the price is $160 per night. What price should the manager set for the rooms to maximize revenue? (ANS: $200.50) 38. For an outdoor concert, a ticket price of $30 typically attracts 5000 people. For each $1 increase in the ticket price, 100 fewer people will attend. The revenue, R, is the product of the number of people attending and the price per ticket. Find the ticket price that maximizes revenue. (ANS: $40) Part F: Cost 39. A showroom for a car dealership is to be built in the shape of a rectangle with brick on the back and sides, and glass on the front. The floor of the showroom is to have an area of 500 me. If a brick wall costs $1200/m while a glass wall costs $600/m, what dimensions would minimize the cost of the showroom? (ANS: sides 5v15 m; back & front 20 15 m) 3 40. A soup can of volume 500 cm is to be constructed. The material for the top costs 0.4 cents/cm* while the material for the bottom and sides costs 0.2 cents/cm". Find the dimensions that will minimize the cost of producing the can. (ANS: r = 5 (24) cm, h = 20 (Tox) (m) 41. The cost of fuel per kilometer for a truck travelling v kilometres per hour is given by the equation C (v) = + 25, What speed will result in the lowest fuel cost per kilometre? (ANS: 50 km/h) 42. Brenda drives an 18-wheeler. She plans to buy her own truck. Her research indicates that the expected running costs, C, in dollars, per 100 km, are given by C(v) = 0.9 + 0.0016v2, where v is the speed, in kilometres per hour. Brenda's first trip will be 1500 km, round trip. She plans to pay herself $30/h. Determine the speed that will minimize Brenda's costs for the trip. (ANS: 97.9 km/h) 43. Glynn is considering buying a truck and becoming a professional driver. The truck manufacturer indicated that he can expect his running costs when driving at v kilometres per hour to be approximated by the function C(v) = 0.85 + 0.0004vz, where the cost, C, is in dollars per kilometre. Glynn plans to pay himself $15/h while he is driving. Finding the speed that will minimize his costs for a 1500 km trip. (ANS: 57.4 km/h) 44. Two buildings in a school complex need to connected with fibre optic cable. Building A is 70 m from a roadway and building B is 200 m down the road. There are two choices in laying the cable. If laid underground, the cost is $1000/m, and if laid above ground, the cost is $500/m. The cable must be laid underground across the playing fields. The cable will be laid from A underground to a point C on the road, and then above ground to B. Where should C be chosen to minimize the total cost of laying the cable? (ANS: 159.6 m from B) . . . cable underground cable above ground A playing field 70 m B road 200 m