tion are given. (a) Sketch the first-quadrant portions ofIn Problems 1–4, a supply function and a demand func-market equilibrium point. (c) Algebraically determine thethose functions on the same set of axes. (b) Label themarket equilibrium point. (c) Algebraically determine themarket equilibrium point.1q2 +101. Supply: p4Demand: p = 86 – 6q – 3g²2. Supply: p = q² + 89 + 16Demand: p = 216 - 293. Supply: p = 0.2q² + 0.4q + 1.8Demand: p = 9 – 0.2q – 0.1q²4. Supply: p q² + 8g + 22%3D%3D%3D1198 4g4Demand: p%3D5. If the supply function for a commodity isp = q? + 8q + 16 and the demand function isp = -3q2 + 6q + 436, find the equilibrium quantityand equilibrium price.6. If the supply function for a commodity isp = q? + 8q + 20 and the demand function isp = 100 – 49 – q², find the equilibrium quantity andequilibrium price.7. If the demand function for a commodity is given by theequation p? + 4q = 1600 and the supply function isgiven by the equation 300 – p² + 2g = 0, find theequilibrium quantity and equilibrium price.8. If the supply and demand functions for a commodityare given by 4p - q = 42 and (p + 2)q = 2100,respectively, find the price that will result in marketequilibrium.9. If the supply and demand functions for a commodityare given by p - q = 10 and q(2p - 10) = 2100, whatIs the equilibrium price and what is the correspondingnumber of units supplied and demanded?%3D%3D%3DaP+ 9g + 10) = 3696, respectively, find the price(p +q)(q+and quantity that give market equilibrium.%3D

Since, you have posted multiple questions, as per guidelines we will solve only first question. If…

Answered: market equilibrium point. (c)…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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QUESTION 7 A company manufactures two types of toys: T1 and T2 using the machines A, B and C. The time required to make T1 is 6, 8 and 12 hours in A, B and C respectively. The time required to make T2 is 8, 4 and 4 hours in A, B and C respectively. The maximum available times for the machine A, B and C are 380, 300 and 404 hours respectively. The profits on T1 and T2 toys are 5 and 3 OMR respectively. Let x = number of toys (T1); y = number of toys (T2). The constraint for the time on machine Ais 8x + 6y ≤ 380 6x + 8y ≥ 380 8x + 6y ≥ 380 6x + 8y ≤ 380
Question 5 A firm's price in a perfectly competitive market is 1000. Its cost function is C(x) = 0.01x³ – 3x² + 1108x + 960, where x ≥ 0 is the number of units produced and sold. (a) Find an expression for the profit function (x) for x ≥ 0. (b) Find all stationary points and determine the profit maximising level of output. (c) Using a sign diagram, determine the intervals over which (x) is increasing and decreasing. (d) Determine the intervals over which 7(x) is concave and convex. (e) Where is the point of inflection in C(x) ? Give an economic interpretation of the point of inflection.
D and 3
Question 5 A firm's price in a perfectly competitive market is 1000. Its cost function is C(x) = 0.01x³ 3x² +1108x + 960, where x ≥ 0 is the number of units produced and sold. (a) Find an expression for the profit function (x) for x ≥ 0. (b) Find all stationary points and determine the profit maximising level of output.
Question 3: (a) Demand for a product is determined by the function p = 32 - 0,01q. What is the price and the quantity of the product under the maximum revenue?(b) Revenue is determined by the function R(q) = 46q - q2, cost is determined by the function C(q) = 5q2+ 10q + 3. Find the maximum revenue and profit. (c) A company sells jeans for $85 each. If the cost of the production is determined by the formula C(q) = q2 + 25q+50, then, how many jeans we need to produce and sell in order to maximize profit?(d) The cost of the production is determined by the formula C(q) = 2q2 + 12q + 30. How many products we need to produce in order to maximize profit, provided that the price of the product is $60? (e) T-shirts are sold for 46 soms each. Provided that the cost of the production is determined by the function C (q) = 120 + 30q + 0,1q2, find the highest possible profit.
42. Offshore Crude Oil Production: Mexico The following table shows daily offshore crude oil production by Pemex, Mexico’s national oil company, for 2008–2014 (t 5 0 rep-resents 2008):6Year t (year since 2008)0 1 2 3 4 5 6Offshore Crude Oil Production s1t2 (million barrels/day)2.25 2.01 1.94 1.90 1.90 1.90 1.85a. Find s102, s122, and s142. Interpret your answers.b. Find s1422s102. Interpret your answer. 43. Social Website Popularity: Twitter The following table shows the popularity of Twitter among social media sites as rated by StatCounter.com (t is the number of years since the start of 2008):7Year t (year since start of 2008)1 2 4 5Twitter Popularity p1t2 (%)7 6 6 7a. Represent p graphically, and then use your graph to estimate p14.52. Interpret your answer.b. One of the following models fits the data almost exactly. Which model is it?(A) p1t25 0.4t32 4t21 12.5t 1 15(B) p1t25 20.33t21 2t 2 8.7(C) p1t25 20.4t31 4t22 12.5t 1 15(D) p1t25 0.33t22 2t 1 8.7 44. Social Website…

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