Please help me figure out these problems! Thank you!
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3. Nelson Sporting Inc., makes three different types of baseball gloves: a regular model, a deluxe model, and a catcher’s model. Each month, the firm has 350 hours of productiontime available in its cutting department, 270 hours available in its finishing department, and90 hours available in its packaging department. The production time (in hours) requirements per glove are given in the following table: ‘ Cutting Finishing PackagingRegular Model 1 1/2 1/6Deluxe Model 1/4Catcher’s Model 1/4 Nelson Sporting Inc. sells regular model $9.5 per glove, deluxe model $14 per glove, andcatcher’s model $11 per glove. On the other hand, a regular model uses $1.5 worth ofraw materials per glove, a deluxe model uses $3.5 worth of raw materials per glove, and a catcher’s model uses $2.5 worth of raw materials per glove. Demand for deluxe and catcher’s models are unlimited, but at most 250 units of regular models can be manufactured each month. Formulate a linear programming model that can be used to determine the number of units of each model that should be produced in order to maximize Nelson Sporting Inc.’s profit. 4. For the following linear programming problem: max 53; + 5y st.63 + 3y 5 242:1; + 4y 5 20—2y 5 —4 $,y>0 a) Show extreme (corner) points and feasible region in your graph.b) Solve the problem using the graphical method, and find the optimal solution. 0) What is the optimal value of the objective function?
