Hinkel Rotary Engine, Ltd., produces four- and sixcylinder models of automobile engines. The firm's profit for each four-cylinder engine sold during its quarterly production cycle is $1,800 – $50X1, where X1 is the number sold. Hinkel makes $2,400 – $70X2 for each of the larger engines sold, with equal to the number of six-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, whereas six-cylinder engines take 130 hours to manufacture.

Formulate this production planning problem for Hinkel.