linear programming problem

Og is the leader of the surprisingly mathematically advanced, though technologically run-of-the-mill, Calm Waters caveman tribe. He must decide on the number of stone clubs and stone axes to be produced for the upcoming battle against the neighboring Peaceful Sunset tribe. Experience has taught him that each club is good for, on the average, 0.45 kills and 0.65 maims, while each axe produces 0.70 kills and 0.35 maims. Production of a club requires 5.1 lb of stone and 2.1 man-hours of labor while an axe requires 3.2 lb of stone and 4.3 man-hours of labor. Og’s tribe has 240 lb of stone available for weapons production, and a total of 200 man-hours of labor available before the expected time of this battle (that Og is sure will end war for all time). Og values a kill as worth two maims in quantifying the damage inflicted on the enemy, and he wishes to produce that mix of weapons that will maximize damage.

(a) Formulate this as a linear programming problem. Make sure to define your decision variables.

(b) Represent this problem graphically, making sure to identify all the feasible corner points and the infeasible corner points.

(c) Solve the problem graphically.

(d) Solve the problem using the computer.

linear programming problem