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Group (A) Answer any TWO 2x10 = 20 1

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Group (A) Answer any TWO 2x10 = 20 1. Find the optimum commodity purchase for a consumer whose utility function is U=f6 ) = 2*, prices per unit of X and X; are Rs. 10 and Rs. 50 respectively. And her total income is Rs. 100. 2. Let the demand (D.) = 9 -p-4p'(t) +p" (t) and supply (5:)=-1 + 4p. Market being perfectly competitive, find the time path of price (p) where p(0) = 4 and p'(0) = 4. 3. Find the primal solution of the following linear programming problem using simplex table method. Max: = 40x, +30x, Such That: * $ 16 ; *; 58: *;+x: 524 ; and * .*: 20 Group B (58-40) Answer any EIGHT 8X5=40. 40 Find the derivative of f(x) = (6x + 2x) (5x-10x'+18x*-4) 2x + 1 dx 5. Evaluate the definite integral of!, ** + 2x 6. Define convex set using algebraic notation method. Z A monopolist uses one input x which he purchases at a fixed price (r) = 5 to produce his output . His demand and production functions are p=85 -3 and q=2 /x respectively. Determine the values of p, and x at which the monopolist maximizes his profit. 8 Solve the first order difference equation yr - Sy- (yo-74) 4 9. Given the pay-off matrix A- find the optimal strategies for the players. 2 1