Oakton Manufacturing makes two types of rocking chairs specifically designed for men and women known as the His and Hers models. Each chair requires four legs and two rockers but differing numbers 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, 1,200 short dowels, and 1,056 long dowels available. The company wants to maximize its profit 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 for this problem.

c. Find the optimal solution.