Question

A furniture factory produces two types of desks. Type I and type II, in the cutting and assembly departments. the number of hours available in each department is: in department A 624 hours and in department B it is a third (1/3) more hours than in department A. To manufacture a type I desk unit it takes 3 hours in department A and 8 hours in department B. To manufacture a type II desk unit, 10 hours are required in department A and 5 hours in department B. If the utility for each type II desktop is $ 500,000.00 and the utility of the desk Type I is 20% less than Type II. How many units of each type of desk should be manufactured to MAXIMIZE utility.

Question: If a new restriction is given: 2x₁ + x₂ < (less or equal) 404 , Is the solution still optimal feasible? If not, what is the new feasible solution? (explain your answer)

Answer 1

Solution:

Let x1 be the number of units of type 1 and,
Let x2 be the number of units of type 2.

Hence, the objective function is,

Z = 500000x2 + 400000x1

subject to,

3x1 + 10x2 <= 624
8x1 + 5x2 <= 832

x1,x2 >=0 both integers.

Hence,

After adding the new constraint we get the same solution as the one stated above.

Hence, to maximize the utility the number of units to be produced are as follows,

x1 = 80
x2 = 38