Hinkel Rotary Engine, Ltd., produces four-, six-, and eight-cylinder models of automobile engines. The firm's profit for each four-cylinder engine sold during its quarterly production cycle is $1,800 - $50X1; where X, is the number of four- cylinder engines sold. Hinkel makes a profit of $2,400 - $70X2 for each of the six-cylinder engines sold, with X2 equal to the number of six- cylinder engines sold. The profit associated with each eight-cylinder engine is $1,950 - $65X3, where X3 is equal to the number of eight-cylinder engines sold. There are 5,000 hours of production time available during each production cycle. A four-cylinder engine requires 100 hours of production time, a six-cylinder engine takes 130 hours, and an eight-cylinder model takes 140 hours to manufacture. Formulate this production problem for Hinkel and solve it by using Excel. Use several different starting values for the decision variables to try to identify a global optimal solution.