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(1) The constrained optimization problem is written as:

Maximize $300B + $500D

Subject to the constraints

Grinding hours: 2B + 5D 800

Drilling hours: 3B + 2D 400

Polishing hours: 2B + 4D 480

Loose constraint is grinding hours. 800 560 = 240 hours

1. Ralph Inc. manufactures two different models of product: basic and deluxe. The miniature tables and chairs provide $300 and $500 of contribution margin, respectively. The models pass through three sequential processes: grinding, drilling, and polishing. Ralph can sell all that it produces of either model. Data pertaining to these processes and market demand are given below (weekly data) Resources Resource available 800 hours 400 hours 480 hours Resource usage by Basic Modelby Deluxe Model Resource usage Grinding hours Drilling hours Polishing hours 2 hours 3 hours 2 hourS 5 hours 2 hours 4 hours (1) Express Ralph's constrained optimization problem as a linear programming model. (Note (2) The optimal product mix is to produce 80 units of basic models and 80 units of deluxe (3) The demand for each model is uniformly spread out over the five-day work week. Ralph solving the problem is not required.) models per week. How much excess capacity per week does the loose constraint have? requires a 1.5-day buffer. Illustrate the DBR structure for Ralph (identify the drummer, the rate of production, the time buffer, and the rope)

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