Oakton Manufacturing makes two types of rocking chairs specifically designed for men and women known as His and Hers models. Each chair requires four legs and two rockers but differing number of wooden dowels. Each His chair requires four short dowels and eight long dowels while each Hers chair requires eight short dowels and four long dowels. Each His chair contributes $10 in profit while each Hers chair contributes $12. The company has 900 legs, 400 rockers, 1200 short dowels, and 1056 long dowels available. The company wants to maximize its profits while also ensuring that it makes at least half as many His chairs as Hers chairs.

a) Formulate an LP model for this problem

b) Sketch the feasible region

c) Find the optimal solution and objective value