Given that q f(p), maximize profits by (a) finding the inverse function p = f(q), (b) using cramer's rule for the first-order condition, and (c) using the hessian for the second order condition. the demand functions and total cost functions are tc qi2q1q2+q q1 100 3p1 +2p2 92 75+0.5p - p2 where q1 and q2 equation are substitute goods, as indicated by the opposite sign for pi and p2 in each

An ideal otto cycle has a compression ratio of 8. at the beginning of the compression process, air is at 95 kpa and 27°c, and 750 kj/kg of heat is transferred to air during the constant-volume heat-addition process. assuming constant specific heats at room temperature, determine (a) the pressure and temperature at the end of the heat-addition process, (b) the net work output, (c) the thermal efficiency, and (d) the mean effective pressure for the cycle. (4390 kpa, 1730 k; 423 kj/kg; 56.4%; 534 kpa)