Spencer Furniture manufactures two different types of china cabinets: a French P

Question

Spencer Furniture manufactures two different types of china cabinets: a French Provincial model and a Danish Modern model. Each cabinet produced must go through three departments: carpentry, painting, and finishing. These departments have 360 hours, 200 hours, and 125 hours of labor available each week. The firm has a contract with a distributor to produce a minimum of 300 of each cabinet per week (or 60 cabinets per day). An analyst had been consulted to determine a product mix to maximize his daily revenue. The following sensitivity report was generated during the analysis:

Suppose 17 additional hours become available in the carpentry department. How much additional profit can be generated as a result of these additional hours?

Consult the sensitivity report to determine the answer. Enter the exact answer.

Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $E$9 Carpentry: LHS Value 360 11.40 360 33.333333 60 $E$10 Painting: LHS Value 190 0 200 1E+30 20 $E$11 Finishing: LHS Value 112.5 0 125 1E+30 12.5 $E$12 Contract French: LHS Value 60 -9 60 20 33.333333 $E$13 Contract Danish: LHS Value 90 0 60 30 1E+30

Explanation / Answer

For each constraint the column headed Shadow Price tells us exactly how much the objective function will change if we change the right-hand side of the corresponding constraint within the limits given in the Allowable Increase/Decrease columns.

For the Carpentry constraint, if the allowable increase is less than 33.333333 (which is true as the increase is 17 hours), the additional profit will be exactly 11.40 * Increase

= 11.40 * 17

= 193.8

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