A furniture company manufactures desks and chairs. Each desk uses 4 units of woo

Question

A furniture company manufactures desks and chairs. Each desk uses 4 units of wood, and each chair uses 3 units of wood. A desk contributes $400 to profit, and a chair contributes $250. Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. There are 2000 units of wood available.

Let d denote the number of desks produced and let c be the number of chairs produced.

After running Solver, you obtain the sensitivity report. Which of the following interpretations is correct?

The marketing constraint on the number of chairs produced relative to the number of desks is not binding at the solution.

Each unit of wood used in the production process costs the company $90.

If we had one additional unit of wood available, the profit would increase by $90.

If we had one additional unit of wood available, 90 additional units of desks and chairs would be produced at the optimum.

Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$10 Units produced Desks 200 0 400 1E+30 66.66666667 $C$10 Units produced Chairs 400 0 250 50 450 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $B$14 Wood_used 2000 90 2000 1E+30 2000 $B$18 Chairs_produced 400 -20 0 666.6666667 1000

Explanation / Answer

The shadow prices tell us how much the optimal solution can be increased or decreased if we change the right hand side values (resources available) with one unit.

The shadow price for Wood_used is $90. So, if we had one additional unit of wood available, the profit would increase by $90.

Hence, option (c) is correct.

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