MANUFACTURING
Response to the following problem:
Lawn Master produces 19-inch and 2 1 -inch lawn mowers, which it sells to membership warehouses and discount stores nationwide. Each lawn mower is powered by a Briggs and Stratton 3.5- horsepower engine. The 19-inch model is a "side bagger" and requires 40 minutes (2/3 hour) to assemble, test, and package. The 21-inch model is a "rear-bagger" with a variable speed assembly and requires one hour to perform the same operations. Each week Lawn Master can receive up to 200 Briggs and Stratton engines and has production facilities to manufacture up to 1 0 0 variable-speed assemblies. There are four production lines, each working eight hours a day, five days a week, for assembly, testing, and packaging. Each 19-inch model nets Lawn Master a $50 profit, whereas each 21-inch model nets a $60 profit.
a. Formulate and solve a linear programming problem for Lawn Master to determine an optimal weekly production schedule of 19-inch and 21-inch lawn mowers. What is the optimal weekly profit?
b. Determine and interpret the range of feasibility for (i) engines; (ii) variable speed assemblies; (iii) production hours.
c. If an emergency developed so that the amount of production time fell just below the lower limit determined in part (b), what would be the new optimal production schedule?