Question

1) Winkler 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. The table below contains all relevant information concerning production capacities for each operation per day, along with net revenue per unit produced. The firm has a contract with an Indiana distributor to produce a minimum of 300 of each cabinet per week (or 60 cabinets per day). Owner Bob Winker would like to determine a product mix to maximize his daily revenue. Cabinet Style Carpentry (Hours/Cabinet) Painting (Hours/Cab Finishing Net (Hours/Cabinet) Revenue/Cabinet 1.5 28 French provincial Danish modern Department capacity (hours) 0.75 0.75 125 360 200 • Formulate the problem as a linear program.

Answer 1

ANSWER:

As per the given Question

Let $X_{1}$ = the number of French Provincial cabinets produced each day.

   $X_{2}$ = the number of Danish Modern cabinets produced each day.

Maximize

$28X_{1}+25X_{2}$ (maximize revenue)

Subject to:

$3X_{1}+2X_{2}\leq 360$ (carpentry hours available)

$1.5X_{1}+X_{2}\leq 200$ (painting hours available)

$0.75X_{1}+0.75X_{2}\leq 125$ (finishing hours available)

$X_{1}\geq 60$      (contract requirement on F.P. cabinets)

$X_{2}\geq 60$ (contract requirement on D.M. cabinets)

$X_{1},X_{2}\geq 0$ (non-negativity constraints)

Optimal Solution:

$X_{1}=60$ , $X_{2}=90$

Revenue = $3930

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