Carving Creations jointly produces wood chips and sawdust used in agriculture. The wood chips and sawdust are actually by-products of the company’s core operations, but Carving Creations accounts for them just like normally produced goods because of their large volumes. One jointly produced batch yields 3,000 cubic yards of wood chips and 10,000 cubic yards of sawdust, and the estimated cost per batch is $21,400. However, the joint production of each good is not equally weighted. Management at Carving Creations estimates that for the time it takes to produce 10 cubic yards of wood chips in the joint production process, only 2 cubic yards of sawdust are produced.

Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $1.75, and the profit for each model B grate is $1.25. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day. Maximize      P = 1.75x + 1.25y subject to   3x  +  4y  ≤ 1000      Resource 1   6x  +  3y  ≤ 1200   Resource 2       x  ≤ 180   Resource 3       y  ≥ 0         x  ≥ 0   (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)$ (b) Identify the binding and nonbinding constraints. constraint 1          constraint 2       constraint 3

Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $1.50. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day. Maximize      P = 2x + 1.5y subject to   3x  +  4y  ≤ 1000      Resource 1   6x  +  3y  ≤ 1200   Resource 2       x  ≤ 180   Resource 3       y  ≥ 0         x  ≥ 0   (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)$  (b) Identify the binding and nonbinding constraints. constraint 1           constraint 2        constraint 3

A small company manufactures three different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of assembly; component B requires 3 hours of fabrication and 1 hour of assembly; and component C requires 2 hours of fabrication and 2 hours of assembly. The company has up to 900 labor-hours of fabrication time and 700 labor-hours of assembly time available per week. The profit on each component, A, B, and C, is $7, $8, and $10, respectively. How many components of each type should the company manufacture each week in order to maximize its profit (assuming that all components manufactured can be sold)? What is the maximum profit? Let x₁, x2, and x3 be the numbers of components A, B, and C, respectively, that get manufactured. Construct a mathematical model in the form of a linear programming problem. Maximize P=[ subject to X1, X₂, X3 20 The company should manufacture (Simplify your answers.) Fabrication time restriction Assembly time restriction…