A sheet of paper 80 cm-by-72 cm is made into an open box (i.e. there's no top), by cutting x-cm squares out of each corner and folding up the sides. Find the value of x that maximizes the volume of the box. Give your answer in the simplified radical form. X= is the max.
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- Which ONE of the following descriptions is CORRECT according to this Normal Form?A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising it sells 250 units. For each additional $2500 spent, an additional 25 units are sold. 1. If x is the amount of money that the company spends on advertising, find a formula for y, the number of units sold as a function of x. y= 2. How many units does the firm sell if it spends $25,000 on advertising? = ____ units 3. How many units does the firm sell if it spends $50,000 on advertising? = ____ units 4. How much advertising money must be spent to sell 700 units? = _____$ 5. Which of the following statements CORRECTLY explains the meaning of the slope? (select all as there may be more than one correct statment) A. If the company spends an additional $1000 on advertising, it will increases the number of units it sells by 10 . B. If the company increases the amount of money it spends on advertising by $250, it…Let say you have 3 products: cake, candy, and bread. The revenue per cake is $8. The revenue per candy is $4. The revenue per bread is $5. Define the number of cake, candy, and bread you are about to produce per day as x, y, and z respectively. The manager wants that the number of cake accounts for at least 30% of the total production per day. What is the correct linear constraint to show this? Group of answer choices 0.3x – 0.7y – 0.7z ≥ 0 0.7x – 0.3y – 0.3z ≥ 0 0.7x – 0.3y – 0.7z ≥ 0 0.3x – 0.7y – 0.3z ≥ 0
- answer that with graphs.Let say you have 3 products: cake, candy, and bread. The revenue per cake is $8. The revenue per candy is $4. The revenue per bread is $5. Define the number of cake, candy, and bread you are about to produce per day as x, y, and z respectively. The manager wants that the number of candy is at least equal to the total number of cake and bread. What is the correct linear constraint to show this? Group of answer choices z – x – y ≥ 0 x – 2y – z ≥ 0 y – x – z ≥ 0 x – y – z ≥ 0A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $5, and the society sells an average of 24 per week at a price of $9 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 3 sales per week. (a) Find a function that models weekly profit in terms of price per feeder. (Let x represent the price per feeder and P represent the profit.) P(x) = (b) What price should the society charge for each feeder to maximize profits? $ What is the maximum weekly profit? $
- Now assume we can derive an economic analysis from the biological relationship. Fisherman select the number of boats to operate - boats will be the choice of EFFORT. Boats Total Harvest 0 (tons) 0 100 200 300 400 500 600 700 800 900 1,200 2,200 2,800 3,000 2,800 2,400 1,600 800 Suppose the price of fish is $1,000 per ton. Suppose the cost to operate a boat for a year is $4,000. Construct a graph showing the total revenue and cost of the fishery. 0 What is the highest profit that can be earned, and how many boats are used for this? ( What is the corresponding long-run stock level associated with the profit-maximizing choice of effort? What is the profit earned if fisherman harvested the MSY? What number of boats are used in open access?For a certain company, the cost for producing x items is 60x + 300 and the revenue for selling x items is 100x – 0.5x². - The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratio polynomial.) Part b: Find two values of x that will create a profit of $300. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x – 1). The order of the list does not matter. To enter va, type sqrt(a). x = Part c: Is it possible for the company to make a profit of $15,000?Technology B uses 4 workers and 2 tonnes of coal to produce 100 meters of cloth. The worker's wages cost $10 and coal costs $5. We have previously calculated that the total cost of production is $50 and that the vertical intercept of the isocost line is 10.If there was a technology that used 1 more worker, how much would it have to decrease the coal required in order to cost the same? (Note: this is the absolute value of the slope of the isocost line.)
- Experiment with manipulating the shape of the line given on the following graph by selecting and dragging each endpoint.Is the function v(x1,x2)=x21x32 a monotonic transformation of u(x1,x2) ? Select one: a. No b. YesThe revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x)=64x-0.020x² 0≤x≤3200 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. ... (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. 23 (Round to one decimal place as needed.) (B) R'(x) =
