1.The cost of gym membership, C, in Australian dollars (AUD), in Paolo’s Gym can
be modelled by the function
C = 65t
C = 65t + 30
where t is the time in months.
(a) Calculate the gym membership cost over a six month period.
(b) Sketch the graph of the function C = 65t + 30 for t ≥ 0.
(c) Calculate the time, t, in months, when the total cost reaches 290 AUD.
In the neighbouring Nicolo’s Gym, the initial payment is 75 AUD higher than in
Paolo’s Gym, however the monthly fee is lower at 30 AUD per month.
(d) Determine the number of months it takes for the total cost to be less by
attending Nicolo’s Gym in comparison to Paolo’s Gym.
2.I have a query, can you solve?
1. Sunshine Desserts sell 3 different flavours of exotic Ice-cream (Lychee surprise, Kumquat ripple and
(Lychee surprise, Kumquat ripple and Avocado 99). Three salespersons Joan, David and Tony each sold the following units, in 100 litre tubs, as shown below
Lychee surprise Kumquat Ripple Avocado 99
Joan 12 10 20
David 16 12 8
Tony 20 16 10
The total sales of each salesperson were £9,800, £8000, and £10,300 respectively. Calculate the cost of each type of ice-cream.
4.You make very good pizzas, so you decide to sell your pizzas on campus. Since the set up for making
pizza is already available to you, the only cost involved is that of making the pizza, which you calculate to be $ 5 per pizza.
a. What is the cost function?
If 10 pizzas are available in a day, the market offers a price of $ 11 per pizza. If 50 pizzas are available in a day, the market offers a price of $ 7 per pizza.
b. Assuming a linear relationship between price and quantity, find the price that the market offers as a function of the number of pizzas available. You start selling the pizzas.
c. What is revenue as a function of the quantity you sell? What is the profit function?
d. What quantity will maximize your profit? Call it q ∗ 1. What is the maximum profit?
e. If somebody is already supplying 5 pizzas every day, What is the maximum profit that you can make?
5.Suppose that Wegboys has a supermarket with a downward sloping demand curve in Pilgrim City. It purchases frozen turkeys
chases frozen turkeys at a constant wholesale price of $1/turkey, which is its full marginal cost for supplying turkeys. During July, only a small number of wealthy people are interested in buying turkeys in Pilgrim. Their demand curve is P = 10 – .02 Q, where P is Wegboys’ retail price for turkeys during the month and Q is the quantity of turkeys purchased. The demand curve for these wealthy people is constant – it is the same curve in both November and July. During November, a large number of less wealthy people enter the market to purchase turkeys for Thanksgiving. Their demand curve for Wegboys’ turkeys is
P = 4 – .0005Q. In other months of the year, they do not purchase turkeys at any price.
a. (5 points) What price should Wegboys charge in July to maximize its profits? Calculate its profits from turkey sales.
b. (5 points) Demonstrate that Wegboys can earn a higher profit if it lowers its retail price for turkeys during November (you can do this without finding the optimal price). Explain the basic economic intuition.
6.Hello I have two problems to solve the subject is Quantitative Methods for Decision-Making
After graduating from AUD, Salman plans
After graduating from AUD, Salman plans to start a book publishing company in the Media City. He did some research and found that the printer will cost Dh 230,000. He estimated that the variable cost per book is Dh 170 and the selling price is Dh 390.
a. How many books must he sell to break even? Also calculate the breakeven in dirham.
b. In addition to the costs given above, if he wants to pay himself a salary of Dh 15,400 per year, what is her breakeven point in units and dirham?
c. In the first three months of his business, he sold 400 books. Suddenly the printer breaks down. He spent Dh 25000 to fix the printer. In addition to 400 books sold, how many more books she should sell to breakeven? Assume that this part of the question is independent, and she does not draw any salary.
A furniture store makes tables and chairs from plywood and glass. The store has 30 units of plywood, 24 units of glass. Each table requires 7 units of plywood three units of glass, whereas each chair requires three units of plywood and two units of glass. The demand for chairs is between 2 and 4. The ratio between the table and chair is at least 1 to 2. A table earns $225 in profit and a chair, $145. The store also wants a minimum profit of $5000. The store wants to determine the number of tables and chairs to make in order to maximize profit. Formulate a linear programming model for this problem