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determine market equilibrium price and quantity, Problem Set A 1. Allina opens an exotic bakery. Her capacity for the month is eight hundred (800) Love Cherry Short cakes. On average, in a month, she pays a fixed amount-for watet. electricity, security and a. loan of TTD100.00, TTD1,200.00, TTD2,700.00 and TTD4,000,00 respectively, In addition, she estimates that TID 50.00 more must be paid for each Love Cherry Short cake she makes and sells. If she sells one Love Cherry Short cake for TID90.00. Identify and elearly state all variables used. Determine the following: a) Allina's total cost and revenue functions. 14 marks] b) From part a) state the domain and range the total cost and revenue functions. 13 marks] e) Allina's total cost when she produces and sells one thousand Love Cherry Short cakes. [1 mark] d) the value of the rational function of total cost and total revenue when no Love Cherry Short cakes are made and sold. 12 marks] 2. Given the functions: h(x)=91r+xandw(x)=13x2 Determine the value(s) for the following: a) h(4) 12 ntarks] b) hw(3) 14 marks] c) w1(0) [4 marks] 3. The government of Antigua wishes to introduce income tax to increase government revenue. In xo doing a consultant was hired to make recommendations on the best way forward. The consultant proposed that the govemment shouldn't tax any employee. earning below XCD25,000.00 annually or the employee first XCD25,000.00 annually. Thereafter, any employee earning between XCD25,000.00 and XCD 40,000.00 annually should pay 5.5% income tax and then any employee earning above XCD 40,000.00 should pay 10.5% income tax. For the above information a) Derive a mathematical function to represent the consultant's position clearly identifying all variables and intervals. [5 marks] b) From part a) above, state the name of ALL the mathematical functions derived. 12 marks] c) If Jane (someone working in Antigua) pays XCD750.00 in income tax, calculate Jane's annual income. [3 marks]