Answer all please

1. Suppose that the cost of producing :11: units of an item is given by C(35) = 1400 + 1505!: 1.25122 + 0.001533 and that the demand function is pc) = 990 33.3. a. Find the profit function. 13(3). h. Find the production level that will maximize profit. 2. The total cost of producing :1: units of a certain item is C(m] (in thousands of dollars}1 where Ola-'1 a: that will minimize the average cost if the company has agreed to produce between three and fifteen units of the item. C(m) = $3 203:2 + 1799: + 242.IfA{.-1:) = is the average cost function. determine the level of production Read the following before attempting exercise 3. Definition: It C(93) is thetotal cost of producing 9: units of a commodity. then the marginal cost of producing 5.23 units is the derivative. 011930 + h) C(30) c" = 1' {so} a l. C .1: +31 C a: ltmg is large and h is small. then 01:30) E w. In particular. lift 2 1. we have Citing] % 00120 + 1) C(30). This represents the cost of producing the [.123 + If? unit. So. it an; is relatively large. Cfr (mg) approximates the cost of producing the (mg + 1)\"ff unit of a commodity. Similarly. it Rho) is the revenue generated by producing :3: units and Ps) is the corresponding profit. Rie] is the marginal revenue approximating the additional revenue generated by producing one more unit and P'fm) is the marginal profit approximating the additional profit obtained by producing one more unit. 3. Acompany estimates that when m units of a particular item are produced. the total cost will be C(23) = $132 + 333 + 98 dollars. They also project that in order to sell all .1: units. the price needs to be 33(3) = %{?5 .1\") dollars per unit. a. Determine the marginal cost function and the marginal revenuefunction. b. Use the marginal cost function to estimate the cost of producing the ninth unit. c. Determine the actual cost of producing the ninth unit. d. Use the marginal revenue function to estimate the revenue derived from the sale of the ninth unit. e. Determine the actual revenue derived from the sale of the ninth unit. 4. A manufacturer of cell phones estimates that when :1: hundred phones are produced. the total profit will be 10(3) = 0.00351:3 + 0.07%2 + 2551: 200 thousand dollars. a. Determine the marginal profit function. b. Use the marginal profit function to approximate the additional profit obtained from increasing production from i. If] to 11 hundred units ii. 50 to 51 hundred units iii. 80 to 81 hundred units c. Use the results from part b) to suggest a production level for this company. 5. Asmall company makes tshirts. They can be produced for $2fshirt. The shirts have been selling for $5 each and at this price tourists have been buying 4000 shirtsfmonth. The owner plans to raise the price of shirts and expects that for each 31 increase in price 400 fewer shirts will be sold each month. What price should be charged per shirt to maximize profits? 5. A bus company will charter a bus that holds 50 people to groups of 35 or more. It a group contains exactly 35 people. then each person will pay $60. In large groups. everyone's fare is reduced by $1 for each person in excess ot 35. Determine the size of the group for which the bus company's revenue will be the greatest. Y. Aretailer has a bargain bin containing items to be sold at $10 each. At this price they sell 25 items per day. The average retail cost of the items in the bin is $5. To stimulate sales they plan to lower the price [or items in the bin and estimate that [or each 25 cent reduction in the price. 5 more items will be sold each day. How should the items in the items in the bin be priced to maximize total daily protit if the price must remain between $100 and $10.00 per item? 8. lma Farmer has 60 orange trees in her grove and harvests an average ot 400 oranges per tree in one season. She considers planting more trees but knows that the average yield per tree will be reduced by 4 oranges for each additional tree planted on the same acreage. How many trees should lma have in her grove to maximize yield