You manage a 220 unitmotel. All units will be occupied, on average, when you can

Question

You manage a 220 unitmotel. All units will be occupied, on average, when you cancharge $50 per day per unit. Experience shows that for each$1 per day per unit that you increase the price, you will accruetwo vacancies. Each occupied room costs $4 per day to cleanand supply. On this bases, what price, in dollars, should youcharge per unit per day to maximize your profit? This is an example ofmy exam question that is due tonight, and I'm not sure how to workit out. I can't find it in my book, eek! I know thefinal answer is $82, but I really need to know all the stepsbetween since the exam question will have variations. Anyhelp is greatly appreciated! You manage a 220 unitmotel. All units will be occupied, on average, when you cancharge $50 per day per unit. Experience shows that for each$1 per day per unit that you increase the price, you will accruetwo vacancies. Each occupied room costs $4 per day to cleanand supply. On this bases, what price, in dollars, should youcharge per unit per day to maximize your profit? This is an example ofmy exam question that is due tonight, and I'm not sure how to workit out. I can't find it in my book, eek! I know thefinal answer is $82, but I really need to know all the stepsbetween since the exam question will have variations. Anyhelp is greatly appreciated! This is an example ofmy exam question that is due tonight, and I'm not sure how to workit out. I can't find it in my book, eek! I know thefinal answer is $82, but I really need to know all the stepsbetween since the exam question will have variations. Anyhelp is greatly appreciated!

Explanation / Answer

this one ends up being the graph of an inverted parabola OUR N IS THE DOLLARS OVER 50 TO CHARGE FOR RENT, f(n) isthe profit with the y-axis being PROFIT, a function ofprice, NUMBER OF ROOMS, AND COST TO CLEAN and the x axis being the price of each room over$50, so , f(n) = (220-2n)(50 + n) - 4(220-2n) (number of rooms rented)(rent) less cost of cleaningroom simplify and graph, remember n is the amount over $50, f(n) isthe amount earned see if this helps you bring it home I went ahead and simplified this equation and used thequadratic formula to find the zeroes of the equation [another name for the two x-intercepts] if you averagethese you will get the x-value of the vertex, plug that in and you get the max profit remember that if the question is what to charge for rooms torent....our n of the vertex is not the answer we have to add 50 to that, so if your 82 is correct (thatmeans the n of the vertex is 32) that is the number I got... this took some time, so please honor me with an appropriaterating. Some things to remember, if you have equations with aquadratic term (x^2) and the coefficient is a negative value then the graph is an inverted parabola, meaning it will have amaximum. So if you find the two x-intercepts and average them, you havethe x of the vertex. Plug that value in and you get the maximun of an invertedparabola. Note: you really cannot charge a negative amount for therent, so any value less than zero is theorectical notpractical. If graphing this, I would start with only the first quadrantand the x axis at the bottom and y axis at the left side. [no need for the other three quadrants---they are notpractical.]

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.