(a) The teachers of a school class are planning to rent busses and vans for a class trip. Each bus can transport 40 students, requires 3 chaperons, and costs RM1, 200 to rent. Each van can transport 8 students, requires 1 chaperone and costs RM100 to rent. There are at least 400 students in the class who are going to the trip and at most 36 parents have volunteered to serve as chaperons. Formulate a linear programming problem to minimize the total cost. Then, solve the linear programme problem. Note: Graph the constraints on a non-graphical paper. The Formula Table is Given Below MATHEMATICAL FORMULA Linear Equations (i) (ii) (iii) (iv) Slope of a line, m= Y-Y X-X Point-slope form, y - y = m(x-x) Slope-intercept form, y=mx+b (where m = slope, b = y-intercept) General form, Ax+By+C =0 (20 marks) Mathematics for Finance a) Simple Interest (1) Accumulated amount, A = P (1 + rt) Where P = principal, r = interest rate, t = number of years Interest, /= Prt b) Compound Interest (1) (ii) Accumulated amount, A = P(1 + i)" Present value for compound interest, P = 4(1+i)" Where i= , n = mt, and m = number of conversion periods per year m c) Effective Rate of Interest d) Annuities (1) Notations: i and n = mt m Future value of an annuity (1 + i)" [ =1] S = R * = [ + ] - m Where S future value of ordinary annuity of n payments of R dollars periodic payment e) Sinking Fund and Amortization Notations: and n = mt (1) m Sinking Fund formula Si R= (1+i)" - 1 Where R periodic payment required to accumulate S dollars over n periods Present value of an annuity 1-(1+i)" P = R Where P = present value of ordinary annuity of n payments of R dollars periodic payment Amortization formula Pi R = 1-(1+i)" Where R= periodic payment on a loan of P dollars to be amortized over n periods