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- Fig 2.1 illustrates the law of diminishing returns in seeking the optimum system (or component) performance and hence the need to balance the performance against the cost. Give examples of two pairs of characteristics other than performance versus cost where optimizing one frequently competes with the other, and briefly explain why they do.A used car dealership rents 210 cars for $9 a day. They want to increase the price to maximize their profits. They notice that if they increase the price by $1.25 that they have fewer rentals. Create an equation for profit for the car dealership rental sales. Determine the price of the rental that maximizes profitfunction for the lightweight compasses is given by p = 40- 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Type your answer here:
- Ruff makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 208 grams of protein and at least 142 grams of fat. If chicken costs 10c per ounce and grain costs 1e per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize costs? (chicken, grain) = What are the shadow costs of protein and fat? ¢ per g e per g protein fatKendra bought 208 donuts for $80. Her profit was $45 once she had sold 100 donuts. Which equation below represents Kendra's profit P(n). as a function of the number sold, n?Spark Studio produces commercials for other companis. A 2-minute commercial, for example, needs exactly 5 minutes of filming and 8 minutes of editing. Let x1 denote the minutes of filming and x2 denote the minutes of editing. a) Suppose that filming costs $45 per minute and editing costs $10 per minute. To produce a 5-miunte commercial, how many minutes of filming and how many minutes of editing Does Spark studio need to minimize cost? How much is this cost? Draw a graph of the isoquant and isocost line to show this optimal bundle. b) Rocket Media, another commercial production company, uses a different technology. The length of commercials it produces is equal to the longer of the two: one-third of the length of filming and one-fourth of the length of editing. When w1 = 15 and w2 = 10, derive Rocket Media's cost function c(y).
- Solve the following problems related to optimization problemsA restaurant finds that, when priced at $8, it sells 60 sandwiches a month. For every dollar that the restaurant discounts their sandwiches, they sell 5 more per month. If the cost to the restaurant to make a sandwich is $4, find the price that the restaurant should charge for a sandwich to maximize its profit. must show all stepsAssume the cost of making 30 belts $800 the cost of makin 35 belts $900 and the cost equation is linear. The belts are sold for$ 27 each. a)find the marginal cost b)find a linear equation in slope-intercept, form that represent the total Cost of making will c) What is the fixed cost? d) find a profit in slope- intercept that will represent the profit if x belt are made and sold? e) Find the break even point?Define the following
- F a) Draw the demand process cycle and label it fully. b) A door company has the following materials in inventory. Inspect the table below and answer the following questions Material Average (in Kilograms) Price Aluminum 3884 $3.0 Steel 5850 $1.4 Iron 200 $1 Work in Progress Average Price Fence 78 230 Final Products Average Price Door 300 300 Window 550 240 i. Calculate the number of turns. ii. Calculate the cost per day.Suppose that the cost function for a commodity is C(x) = 40 + x2 dollars. (a) Find the marginal cost at x = 4 units. MC(4) = Tell what this predicts about the cost of producing 1 additional unit. The cost to produce the 5th unit is predicted to be $ (b) Calculate C(5) – C(4) to find the actual cost of producing 1 additional unit. Need Help? Read It Watch Itwhen samsung reallocates its resources to produce 3.75 million tablets instead of 2 million tablets the opporunity cost a. 1.75 million tablet b 1.75 million phone c. 7 million phone d.7 million tablet