SAT College

Prices to a concert cost N$200 for an adult and N$150 for a child, the concert venue can accommodate at most 240 people. The organizers are giving a N$20 discount to every adult and N$10 discount for every child but do not want the total discounted amount to exceed N$3200. Draw a graph and use it to answer the following questions: i. How many tickets altogether should the organisers sell in order to maximise their sales amount? ii. How many tickets of each type (adult and child) should they sell to get a maximum sales amount? iii. What is the maximum sales amount the organisers can make? iv. If the profit is calculated as follows: profit = total sales – total discount amount. How much profit will the organisers make from the maximum sales? Overall presentation (neat, clear and well presented)

Answers

Answer 1

Answer:

i. 240 tickets

ii. 80 adults and 160 children

iii. N$ 40,000.00

iv. Profit= N$ 36,800.00

Explanation:

Ok so in order to solve this problem we need to start by building our system of equations from the restrictions the problem gives us:

let's say that

x=# of adult tickets

y= # of children tickets

so

"... the concert venue can accommodate at most 240 people."

this translates to the following inequality:

[tex]x+y\leq240[/tex]

"The organizeres are giving a N$20 discount to every adult and N$10 discount for every child but do not want the total descounted amount to exceed N$3200."

Translates to

[tex]20x+10y\leq3200[/tex]

and we know we cannot sell a negative number of adult and children tickets so the last restrictions are:

[tex]x\geq0[/tex]

[tex]y\geq0[/tex]

so we can now graph our system of inequalities (see graph attached)

the procedure to graph a linear equation is as follows:

1. Pick an x-value

2. Find the corresponding y-value with the provided equation we need to graph.

3. Write the coordinates as an ordered pair (x,y)

4. Repeat the process with a second x-value.

5. Graph the two points you found on the previous steps.

6. Connect the points with a straight line.

So the feasible region is the one that all restrictions will have in common and the maximum and minimum points for our objective function will be the marked points, which are the vertices of the feasible region. So we test them to see which will maximize our objective function.

Objective function:

s=200x+150y

(0,0)

s=200(0)+150(0)=0

(0,240)

s=200(0)+150(240)=N$36,000

(80,160)

s=200(80)+150(160)=N$40,000

(160,0)

s=200(160)+150(0)=N$32,000

So when comparing the results we can see that the objective function will be maximized at the point (80,160) so:

i) How many tickets altogether should the organisers sell in order to maximize their sales amount?

total # of tickets = x+y = 80+160=240 tickets

ii) How many tickets of each type (adult and child) should they sell to get a maximum sales amount?

x                                   y

80 adult tickets and 160 child tickets.

iii) What is the maximum sales amount the organizers can make?

s=200(80)+150(160)=N$40,000

iv) If the profit is calculated as follows: profit = total sales - total discount amount. How much profit will the organisers make from the maximum sales?

Profit= total sales - total discount

total sales=200(80)+150(160)=N$40,000

total discount = 20(80)+10(160)=N$3,200

Profit=N$40,000-N$3,200=N$36,800.00

Prices To A Concert Cost N$200 For An Adult And N$150 For A Child, The Concert Venue Can Accommodate

Related Questions

Other Questions
All of the following are TRUE of the prosecution EXCEPT *Represents the governmentBrings criminal chargesRepresent the defensePresents evidence to the court On January 1, 2021, the general ledger of Big Blast Fireworks includes the following account balances:Accounts Debit Credit Cash $ 25,700 Accounts Receivable 46,000 Allowance for Uncollectible Accounts 4,100 Inventory 49,000 Land 90,100 Accounts Payable 25,700 Notes Payable (6%, due in 3 years) 49,000 Common Stock 75,000 Retained Earnings 57,000 Totals $ 210,800 $ 210,800 The $49,000 beginning balance of inventory consists of 490 units, each costing $100. During January 2021, Big Blast Fireworks had the following inventory transactions:January 3 Purchase 1,750 units for $196,000 on account ($112 each).January 8 Purchase 1,850 units for $216,450 on account ($117 each).January 12 Purchase 1,950 units for $237,900 on account ($122 each).January 15 Return 195 of the units purchased on January 12 because of defects.January 19 Sell 5,700 units on account for $855,000. The cost of the units sold is determined using a FIFO perpetual inventory system.January 22 Receive $837,000 from customers on accounts receivable.January 24 Pay $620,000 to inventory suppliers on accounts payable.January 27 Write off accounts receivable as uncollectible, $2,800.January 31 Pay cash for salaries during January, $138,000.The following information is available on January 31, 2021.At the end of January, the company estimates that the remaining units of inventory are expected to sell in February for only $100 each.The company estimates future uncollectible accounts. The company determines $5,900 of accounts receivable on January 31 are past due, and 35% of these accounts are estimated to be uncollectible. The remaining accounts receivable on January 31 are not past due, and 5% of these accounts are estimated to be uncollectible. (Hint: Use the January 31 accounts receivable balance calculated in the general ledger.)Accrued interest expense on notes payable for January. Interest is expected to be paid each December 31.Accrued income taxes at the end of January are $14,200.Record each of the transactions listed above in the 'General Journal' tab (these are shown as items 1 - 10) assuming a FIFO perpetual inventory system. Review the 'General Ledger' and the 'Trial Balance' tabs to see the effect of the transactions on the account balances.2. Record adjusting entries on January 31. in the 'General Journal' tab (these are shown as items 11-14).3. Review the adjusted 'Trial Balance' as of January 31, 2021, in the 'Trial Balance' tab.4. Prepare a multiple-step income statement for the period ended January 31, 2021, in the 'Income Statement' tab.5. Prepare a classified balance sheet as of January 31, 2021, in the 'Balance Sheet' tab.6. Record the closing entries in the 'General Journal' tab (these are shown as items 15 and 16).7. Using the information from the requirements above, complete the 'Analysis' tab. Convert 84 ounces to milliliters What are the excluded values? x = -3; z = 0 y = -5; z = 0 y = 0; z = -5 none of the above Although they are friends, Huck Finn and Tom Sawyer display different character traits and responses to events and toone another's suggested plans. State one trait of each character that is evidenced in this excerpt. Explain howdifferences between the two characters add to the development and resolution of the episode presented. Includeevidence from the text. The word affect is a _____. nounverb The dean of the engineering school at a technical university wants to emphasize the importance of having students who are gifted at reading and writing as well as math. She wants to know if she can accurately claim that graduate students in engineering programs at her school have significantly higher scores on the verbal reasoning section of the GRE (a standardized test used in the admissions process for many graduate programs) than the national average for engineering students. The national average for the verbal reasoning GRE score for engineering students was 150 with a standard deviation of 9. A random sample of 49 engineering graduate students at her school were found to have an average verbal reasoning GRE score of 153. After analyzing the data to determine whether the mean verbal reasoning GRE score of the engineering graduate students at the technical university is higher than the national average, the p-value of 0.0099 was obtained. Using a 0.05 significance level, what conclusion can be drawn from the data? The kitchen-tile installer has 20 green, 14 beige, and 16 white tiles in a box. What is the probability of picking a beige tile from the box without looking? Whats the surface area of this prism? How did Midway show the value of military intelligence? Bad gums may mean a bad heart. Researchers discovered that 82% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums. Only 33% of healthy people have this disease. Suppose that in a certain community heart attacks are quite rare, occurring with only 15% probability. A. If someone has periodontal disease, what is the probability that he or she will have a heart attack Someone help me with #2 and #3 Can anybody answer these questions. By the way the questions are seperated in different screenshots that i put. Only monks and Nuns are real Buddhists. Do you agree with the statement? Write 5 sentences to explain the answer I need any information on the death of Tupac Shakur I want to investigate this murder myself and see what i can find. The Alexandrian scholar-poet Callimachus a. rejected poetry as unequal to scholarly work. b. rejected Greek philosophy as unequal to the epics of Homer. c. urged poets to write long epic works to rival Homer. d. urged his fellow poets to write short, finely crafted works rather than epics. Calculate Payroll An employee earns $30 per hour and 1.5 times that rate for all hours in excess of 40 hours per week. If the employee worked 54 hours during the week. Assume that the social security tax rate is 6.0%, the Medicare tax rate is 1.5%, and the employe's federal income tax withheld is $295. a. Determine the employe's gross pay for the week.b. Determine the employee's net pay for the week. Round your answer to two decimal places. PLZZZ DO THE PROBLEM THAT HAS THE ORANGE RECTANGLE PLZZZZZZZZZZZ!!!!!!I WILL GIVE BRAINLIEST AND 10 MORE POINTS!!!!! What is meant by the term financial planning?a Long-term goals are reached over an extended period of time, so your current income does not affectthem.b. It is creating a road map of everything you do with your money.c. It is hoping you will have enough money to pay all your bills on time.d. If your income exceeds your expenses, you will be able to save money for the future.Please select the best answer from the choices providedBDSave and ExitNextSubmitMatkathisandrum Read the sentence and choose the option with the correct words that would replace the pronoun in bold type.(Ellas)son atrevidas.Su amiga Matilda y ElenaMi amigo Juan y ElenaMi amiga Matilda y elSu amigo Juan y lellas is bold