Question

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 times per cabinet produced and 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 Winkler would like to determine a product mix to maximize his daily revenue.

Formulate as an LP problem and obtain the revenue      

Bob Winkler wants to add this requirment to his production policy: To produce at least as many French Provencial cabinets as Danish Modern.

How many French Provencial and Danish Modern Cabinets should Bob produce?

What is the impact on revenue of the solution in part d compared to the result in part c?

               

Cabinet Style	Carpentry (hours/cabinet)	Painting (hours/cabinet)	Finishing (hours/cabinet)	Net revenue/cabinet ($)
French Provincial	3	1.5	0.75	28
Danish Modern	2	1	0.75	25
Department Capacity (hours)	360	200	125

Answer 1

Let X1 = the number of French Provincial cabinets produced each day

Let X2 = the number of Danish Modern cabinets produced each day

Formulating LP problem:

Maximize 28X1 + 25X2 (maximize revenue)

Subject to: 3X1 + 2X2 ≤360 (carpentry hours available)

1.5X1 + X2 ≤200 (painting hours available)

0.75X1 + 0.75X2 ≤125 (finishing hours available)

X1 ≥60 (contract requirement on F.P. cabinets)

X2 ≥60 (contract requirement on D.M. cabinets)

X1≥90 (produce at least as many F.P. cabinets as D.M. cabinets)

X1, X2 ≥0 (non-negativity constraints)

Optimal Solution:

X1 = 90 X2 = 45

Revenue

Revenue =28*90+25*45= $3,645

But this solution is not feasible
because the final solution violates the  constraint X2≥60 .

How many French Provencial and Danish Modern Cabinets should Bob produce?

90 number of French Provincial cabinets produced each day.

45 number of Danish Modern cabinets produced each day.

What is the impact on revenue of the solution in part d compared to the result in part c?

Revenue is decreased in part d) as compared to result in part c). But part d solution is infeasible because the constraint of X2> 60 doesn't get satisfied.