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If Qd = 25 -5P and Qs = P. Then, the choke
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- A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price = 150 − 0.01 × Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing) = $50,000 and the variable cost per unit = $40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 6,000 units per year.Suppose your product sells for $1.20 per unit. The total cost of producing x units is C(x) = 50 + 0.20x + .001x^2 dollars. a.) Find the marginal revenue and marginal profit functions b.) Find the marginal profit when x = 400 c.) What is the approximate profit from selling the 401st unit? d.) Find the value of x for which the marginal profit is zero.A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price=160−0.02×Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing)=$47,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 4,000 units per year. The maximum profit that can be achieved is $? (Round to the nearest dollar.) The unit price at the point of optimal demand is $? per unit.
- Your current prices are $311 in the southwestern region, $278 in the western region and $240 in the New England region. Your marginal cost is now $212.21. Given the predicted changes in the quantity demanded by region per problem 1 and using the stay even analysis %ΔQd = %ΔP/[%ΔP + ((P-MC)/P)], can you raise the price by 7% in any of the regional markets?Jimbob’s Garage is the only auto repair facility in a remote area of the Nevada desert. The proprietor, Jimbob, does not post his prices for services. Knowing his customers are travelers who are desperate to get their vehicles repaired, he sizes each one up for their apparent ability to pay, and charges them accordingly.Suppose annual demand for his repair services is Qd = 1000 – .5*P, and his marginal cost per repair job is $80. What is the range of prices he will charge his customers? How many cars does he repair per year? What is his profit if his fixed costs are $12,000/yr?4.Q. The Ali Baba Co. is the only supplier of a particular type of Oriental carpet. The estimated demand for its carpets is Q = 112,000 – 500P + 5M Where Q = number of carpets, P = price of carpets (dollars per unit), and M = consumers’ income per capita. The estimated average variable cost function for Ali Baba’s carpets is AVC = 200 – 0.012Q + 0.000002Q2 Consumer’s income per capita is expected to be $20,000 and total fixed cost is $100,0000. a. How many carpets should the firm produce to maximize profit? b. What is the profit-maximizing price of carpets? c. What is the maximum amount of profit that the firm can earn selling carpets? d. Answer parts a through c if consumers’ income per capita is expected to be $30,000 instead Please answer d only.
- Breakout on Quantity Discounts The price charged for a material depends on the quantity purchased. Determine the optimal order quantity. D = 35,000/yr; A = $100 i = 0.4/yr C1 = $2.85 for 0<= Q <1,000 C2 = $2.65 for 1000<= Q < 5,000 C3 = $2.50 for 5,000 <= QIf discount rate is 0.1, then the discount factor is?Q. The Ali Baba Co. is the only supplier of a particular type of Oriental carpet. The estimated demand for its carpets is Q = 112,000 – 500P + 5M Where Q = number of carpets, P = price of carpets (dollars per unit), and M = consumers’ income per capita. The estimated average variable cost function for Ali Baba’s carpets is AVC = 200 – 0.012Q + 0.000002Q2 Consumer’s income per capita is expected to be $20,000 and total fixed cost is $100,0000. a. How many carpets should the firm produce to maximize profit? b. What is the profit-maximizing price of carpets? c. What is the maximum amount of profit that the firm can earn selling carpets? d. Answer parts a through c if consumers’ income per capita is expected to be $30,000 instead.
- If TC = 98 + 15Q + 6Q2 , what is the marginal cost at when Q=7? Enter as a value.A company estimates that the total revenue, R, in dollars, received from the sale of q items is ? = 3000 + ln(1 + 1000?^3) and the marginal cost is ??(?) = 0.05?^2 − 1.6? + 50. Calculate and interpret the marginal profit if q = 100.Betty runs a toy store. Each toy costs Betty $4 and sells for $10 (so the gross profit per unit sold is $6). Daily demand varies according to the following table: Demand Probability 90 0.64 100 0.24 110 0.12 At the beginning of every day, Betty replenishes shelves with 100 toys (i.e., there are 100 toys for sale every day). If daily demand is less than 100, an inventory holding cost of $0.10 is charged for each toy that is not sold. However, if daily demand is greater than 100, a stockout occurs, and a shortage cost of $0.90 is charged for each unit of demand that cannot be satisfied. Unsatisfied demand is lost. (a) Set up intervals of random numbers that can be used to simulate daily demand. (b) Sketch a simulation table and perform a simulation for 9 days. Use the random numbers 0.76, 0.26, 0.77, 0.57, 0.87, 0.35, 0.50, 0.56, and 0.90 to generate simulated values for daily demand for those 9 days. Based on this sample of 9 days, what is the average daily net profit and service level…