A small workshop has an automatic machine that can operate for a maximum of 5 hours a day. With this machine, we want to manufacture dowels and bolts and we elieves that the market can absorb all production. It is considered that at least 600 units each part must be manufactured. On the other hand, given that the demand for the pegs usually greater than that of the bolts, it is desired that the manufacture of the anchors presents at least 40% of the machine's total output. The data concerning the oduction rates, costs and sales prices are shown in the following table. Rooms Rate Cost of Cost of Price of raw materials labor sale production (units per hour) 300 ($ per unit) 0.03 Peg ($ per hour) ($ per unit) 9 0.16 9 0.20 Bolt 200 0.035 a) Formulate this problem as a linear optimization model. To do this, you need to identify the variables associated with this problem, construct the function objec tif with the aim of maximizing the daily pro ts of the workshop as well as building the various constraints. b) Graph the constraints (dropping the integration constraints) grity) and determine the feasible domain of the