Write the Linear Programming formulations for the following problem
A manufacturer of lawn and garden equipment makes two basic types of lawn mowers: a push-type and a self-propelled model. The push type requires 9 minutes to assemble and 2 minutes to package; the self-propelled model requires 12 minutes to assemble and 6 minutes to package.
Each type has an engine. The company has 12 hours of assembly time available, 75 engines, and 5 hours of packing time. Profits are $70 for the self-propelled model and $45 for the push-type mower per unit.
Formulate the problem as an LP to determine how many of each type of mower to produce.