Answer 1 12:23 PM O OECON1003 Undergraduate ProgramProblem Set A(1) The table below shows the calories, fat, and carbohydrates per ounce for three brands ofcereal, and the total amount of calories, fat, and carbohydrates required for a special diet.Calories Fat CarbohydratesCereal Brand x5022Cereal Brand Y1080.125.5Cereal Brand Z1275.518Total Required3935.791(i) Using the information in the table above, write a system of three equations.(ii) Write a system in matrix form Ar=b.(ii) Using the Cramer's Rule or Inverse Method, find the amount of each brand of cereal that willgive the level of nutrition required.(2) For the function f(x) =-x' -24x+196) Determine the turning points and the values of the function at each turning point.(ii) Determine the point of inflection, any exist.(iii) What is the range of value over which the function is strictly increasing(iv) What is the range of values over which the function is concave upwards.(3) A production manager determines that t months after production on a new product begins,17 +13(2r +1)the number of units produced will be N thousand, where N(1) =(i) What would be the level of production 5 months into operations.(ii) What would be the level of production be in the long run.THE UNIVERSITY OF THE WEST INDIES OPEN CAMPUSPage 19 of 36ECONIO03 Mahematies for the Social Sciences 1-Course laformmation. Academic Year 2021/2022, Semester 1Problem Set B(1) If the total cost of a firm is C(x) =1.5x' -5x + 20.x +5. Find the marginal cost (in dollars)when 25 units are produced and sold.(2) The number q of roller blades a firm is willing to sell per week at a price of $p is given byq = 60p+25 +300 for 20s ps100.(i) Find dgdp(ii) Find the amount supplied when the price is $56.(ii) Find the instantaneous rate of change of supply with respect to price when the price is $56.(3)(i) A broken pipe at an oil rig off the east coast of Trinidad produces a circular oil slick that is Smeters thick at a distance x meters from the break. It difficult to measure the thickness of theslick directly at the source owing to excess turbulence, but for x0 they know thatSCx) --2 '3I+x+2x

Question

Answer 1 12:23 PM O OECON1003 Undergraduate ProgramProblem Set A(1) The table below shows the calories, fat, and carbohydrates per ounce for three brands ofcereal, and the total amount of calories, fat, and carbohydrates required for a special diet.Calories Fat CarbohydratesCereal Brand x5022Cereal Brand Y1080.125.5Cereal Brand Z1275.518Total Required3935.791(i) Using the information in the table above, write a system of three equations.(ii) Write a system in matrix form Ar=b.(ii) Using the Cramer's Rule or Inverse Method, find the amount of each brand of cereal that willgive the level of nutrition required.(2) For the function f(x) =-x' -24x+196) Determine the turning points and the values of the function at each turning point.(ii) Determine the point of inflection, any exist.(iii) What is the range of value over which the function is strictly increasing(iv) What is the range of values over which the function is concave upwards.(3) A production manager determines that t months after production on a new product begins,17 +13(2r +1)the number of units produced will be N thousand, where N(1) =(i) What would be the level of production 5 months into operations.(ii) What would be the level of production be in the long run.THE UNIVERSITY OF THE WEST INDIES OPEN CAMPUSPage 19 of 36ECONIO03 Mahematies for the Social Sciences 1-Course laformmation. Academic Year 2021/2022, Semester 1Problem Set B(1) If the total cost of a firm is C(x) =1.5x' -5x + 20.x +5. Find the marginal cost (in dollars)when 25 units are produced and sold.(2) The number q of roller blades a firm is willing to sell per week at a price of $p is given byq = 60p+25 +300 for 20s ps100.(i) Find dgdp(ii) Find the amount supplied when the price is $56.(ii) Find the instantaneous rate of change of supply with respect to price when the price is $56.(3)(i) A broken pipe at an oil rig off the east coast of Trinidad produces a circular oil slick that is Smeters thick at a distance x meters from the break. It difficult to measure the thickness of theslick directly at the source owing to excess turbulence, but for x>0 they know thatSCx) --2 '3I+x+2x

Accepted Answer

the given system can be written as three equations 
(a) The first equation is based upon the…