The community park has a small lake where visitors can rent paddle boats at $1 for 15 minutes, up to 2 hours. After 2 hours, the rate increases to $3 for 30 minutes.

Problem Write the piecewise function to model this situation and graph the function.

  1. What is the rental charge at 15 minutes? At 16 minutes? At 45 minutes?

2. If you had only $15, how long could you rent a boat?

3. How are the two lines in the graph the same, and how are they different?

4. How would the graph change if the rate change occurred at ? = 1 hour?

5. How would the graph change if the fee were $2 for 15 minutes?

6. What is the rental fee at 3 hours?

1. Jupiter recently introduced her cousin Letecia to one of her colleagues working for the Avocado Park Development Council, whose name is Scheherazade. Letecia has decided to ask Scheherazade out on a date and her goats have jumped in to help. They don’t really understand human romantic customs, but they reason that humans base most of their behavior on money, so they want to start by estimating how much Letecia should expect to spend on a date. They collect a random sample of 52 first dates from residents of Avocado Park and ask how much money the dater spent (they discarded responses of zero as unhelpful). The results of their survey can be found under the questions. Thanks
   1. Identify the population of interest.
   2. Identify the variable of interest. What type of variable is it?
   3. If the goats want to estimate HOW MUCH Letecia should be expected to spend on this date, what parameter should they try to estimate?
   4. If the goats wish to estimate the parameter you chose in part c using a confidence interval, what conditions would need to be met? What assumptions would be necessary?
   5. Estimate the parameter you chose in part c with a confidence level of 90%.
   6. If Letecia can only afford to spend $80 on this date, should she worry that she’ll come off as cheap? Justify your answer.

Date Expense: 43,96, 70, 92, 87, 92, 70, 89, 65, 67, 43, 61, 57, 61, 75, 46, 83, 27, 81, 22, 127, 94, 86, 69, 102, 96, 59, 98, 72, 115, 117, 67, 55, 73, 84, 64, 62, 45, 51, 84, 74, 60, 82, 69, 41, 81, 62, 83, 120, 72, 97, 66

A theme park owner records the number of times the same kids from two separate age groups ride the newest attraction.

Using the computational formula, what is the SS, sample variance, and standard deviation for the age group of 13–16? (Round your answers for variance and standard deviation to two decimal places.)

SS sample variance standard deviation

theme park owner wants to know if the children’s rides are favoring 10 year old girls over 10 year old boys based on height. In other words, does one group taller than the other and thus can go on more rides?

Part a: The owner gathered height data on 10 year old girls and 10 year old boys, see data below. Determine at the 5% significance level if there is evidence that the two genders are not the same height and thus cannot all go on the same rides. Show your work and give your answer in complete sentences in context of the problem.

Part b: After doing some research, the owner found the following information about the expected height and standard deviation for 10 year olds. Does that change the result of part a? Show your work and give your answer in complete sentences in context of the problem.

Stepford Paints makes and sells paint to home improvement stores. Stepford​'s only plant can produce up to 19 million cans of paint per year. Current annual production is 15 million cans. Fixed​ manufacturing, selling, and administrative costs total $27 million per year. The variable cost of making and selling each can of paint is $6.10. Stockholders expect a 20​% annual return on the​ company's $38 million of assets.

Requirement 1. What is Stepford​'s current total cost of making and selling 15 million cans of​ paint? What is the current cost per can of​ paint? Select the formula labels and enter the amounts to calculate Stepford​'s current total cost and current cost per can of paint. ​(Enter currency amounts in​ dollars, not in millions. Enter unit values as whole​ numbers, not in millions. Round all currency amounts to the nearest whole dollar and round the cost per unit to the nearest​ cent, $X.XX.)

Requirement 2. Assume that Stepford is a​ price-taker and the current wholesale market price is $8.60 per can of paint. What is the target total of cost in producing and selling 15 million cans of​ paint? Given Stepford​'s current total​ costs, will the company reach​ stockholders' profit​ goals? Begin by calculating Stepford​'s target total cost. Select the formula labels and enter the amounts. ​(Enter currency amounts in​ dollars, not in millions. Round all currency amounts to the nearest whole​ dollar.)

Given

StepfordStepford​'s

current total​ costs, will the company reach​ stockholders' profit​ goals? ​(Enter currency amounts in​ dollars, not in​ millions.)

Requirement 3. Continuing with Requirement​ 2, let's say that Stepford has found ways to reduce its total fixed costs by $310,000. What is the target variable cost per can of​ paint? Select the formula labels and enter the amounts to calculate Stepford​'s target variable cost per can of paint. ​(Enter currency amounts in​ dollars, not in millions. Enter unit values as whole​ numbers, not in millions. Round cost per unit amounts to the nearest​ cent, $X.XX.)

Requirement 4. Suppose Stepford plans to spend an additional $1.9 million on advertising to differentiate its product in order to increase sales volume to 16 million cans and become more of a​ price-setter. Assume that Stepford did reduce its total fixed costs by $310,000 as stated in Requirement 3 but could not find ways to save on its variable costs. What is the​ cost-plus price for a can of paint under these​ conditions? Select the formula labels and enter the amounts to calculate Stepford​'s ​cost-plus price for a can of paint under these conditions. ​(Enter currency amounts in​ dollars, not in millions. Round cost per unit amounts to the nearest​ cent, $X.XX.)

intermediate microeconomic theory courses, with topics production, cost, and supply

The book used in this course is Intermediate Microeconomics and Its Application, by walter nicholson

The question is :

1. It is known that the total revenue function is ?(?) = 45,75? − ?²
short-run cost function ??? (?) = ?³ - 12? ² + 60? + 40

A. Determine the function: Average cost, marginal cost, Fixed cost, variable cost Average revenue, marginal revenue and determine the demand function and the supply function (q) and draw it in a graph by showing the price and quantity balance

B. Calculate how many q in order to obtain maximum profit, the total income at the maximum profit level, the total cost at the maximum profit level and the maximum profit.

1. A. (EOQ) Calculate the EOQ quantity given:

a. Fixed cost per order of $40

b. holding cost per inventory unit of $2.00

c. estimated demand for inventory of 200,000

Solve EOQ using the information listed above:

B. Calculate the total cost associated the EOQ amount calculated in part A:

C. The company wants to keep Safety Stock of an additional; 8 units. Calculate the cost associated with the safety stock and the total cost of the EOQ amount with safety stock.

Cost of Safety stock:

Total cost with safety stock included:

D. It takes 2 days to get a delivery. Calculate the Reorder point when another order for the EOQ amount should be placed:

1) Suppose that a firm’s production function is q=10L^0.25 K^0.75. The cost of a unit of labor is $30 and the cost of a unit of capital is $90. a. The firm is currently producing 120 units of output. Derive the cost-minimizing quantities of labor and capital (i.e. in the long run). What is the total cost?

b. The firm now wants to increase output to 160 units. If capital is fixed at the level you found in part a) (i.e. in the short run), how much labor will the firm require? What is the firm’s new total cost?

3. What is the cost-minimizing level of capital and labor in the long run if the firm wants to produce 160 units of output? What is the total cost now?

You are trying to decide on the best mode of transportation for your company. You want to balance the cost of faster transportation with holding more inventory. This is because the amount of inventory you must hold is a function of lead time.

It costs $15 per unit per year to hold a product in inventory. The forecasted demand for this product is 10,000 units per year. The total amount of inventory is made up of two types of inventory: safety stock and in-transit. Calculations for determining the average amount of inventory for each type are given below.

Safety Stock Cost = 2 x Average Demand during Lead Time * Holding Cost per Unit per Year

In-Transit Inventory Cost = Total Annual Demand x (Lead Time / 365) * Holding Cost per Unit per Year

Total Cost = Safety Stock Cost + In-Transit Inventory Cost + Transportation Cost

The following is data related to your transportation options.

1. Build a spreadsheet model that calculates the total cost of transportation for Air, Truck, and Rail transportation. Based on your total cost calculations, what mode of transportation would you recommend? What is the total cost of your recommendation?

2. How much would the cost per unit of the other two modes have to change in order to make you change your recommendation?

3. What would the lead time of Rail have to change to in order to make it the best option?

4. Use a one-way data table to show how the total cost of Air transportation changes as demand varies between 2,000 to 20,000 units. For what demand levels is it better to recommend Air transportation over your recommendation to Problem #1?

5. Create a two-way data table showing the total costs at varying levels of transportation cost per unit and lead time for Truck transportation. What does this tell you?
   

6. How does changing the holding cost affect your recommendation to Problem #1?

7. You run a regression and find that your demand actually appears to be related to lead time according to the following equation:

Demand = 10,700 – 100*Lead Time

Assume that you sell this item for $45. Calculate Total Profit for each of the modes of transportation. Does this affect your recommendation to Problem #1? How sensitive is this decision?

You are trying to decide on the best mode of transportation for your company. You want to balance the cost of faster transportation with holding more inventory. This is because the amount of inventory you must hold is a function of lead time.

It costs $15 per unit per year to hold a product in inventory. The forecasted demand for this product is 10,000 units per year. The total amount of inventory is made up of two types of inventory: safety stock and in-transit. Calculations for determining the average amount of inventory for each type are given below.  

Safety Stock Cost = 2 x Average Demand during Lead Time * Holding Cost per Unit per Year

In-Transit Inventory Cost = Total Annual Demand x (Lead Time / 365) * Holding Cost per Unit per Year

Total Cost = Safety Stock Cost + In-Transit Inventory Cost + Transportation Cost

The following is data related to your transportation options.

1. Build a spreadsheet model that calculates the total cost of transportation for Air, Truck, and Rail transportation. Based on your total cost calculations, what mode of transportation would you recommend? What is the total cost of your recommendation?

2. How much would the cost per unit of the other two modes have to change in order to make you change your recommendation?

3. What would the lead time of Rail have to change to in order to make it the best option?
4. Use a one-way data table to show how the total cost of Air transportation changes as demand varies between 2,000 to 20,000 units. For what demand levels is it better to recommend Air transportation over your recommendation to Problem #1?

5. Create a two-way data table showing the total costs at varying levels of transportation cost per unit and lead time for Truck transportation. What does this tell you

6. How does changing the holding cost affect your recommendation to Problem #1?

7. You run a regression and find that your demand actually appears to be related to lead time according to the following equation:

Demand = 10,700 – 100*Lead Time

Assume that you sell this item for $45. Calculate Total Profit for each of the modes of transportation. Does this affect your recommendation to Problem #1? How sensitive is this decision?

SHOW EXCEL WORK