Question

The management of MACU Corporation is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor availability, labor utilization, and product profitability:

Department	Product (hours/unit) 1                            2	Labor-Hours Available
A	1.00                                  0.38	110
B	0.25                                  0.30		45
C	0.25                                  0.45		60
Profit contribution/unit	$30.00                                  $15.00

What are the optimal (maximum profit) production quantities for the company?

a.   What type/s of model/s should be used to solve the problem and why would you use that model/s? (20 points)

b.   Develop a model of the MACU Corporation problem. Solve the model to determine the optimal product quantities of products 1 and 2. (60 points)

c.   In computing the profit contribution per unit, management did not deduct labor costs because they are considered fixed for the upcoming planning period. However, suppose that overtime can be scheduled in some of the departments. Which department would you recommend scheduling for overtime? How much would you be willing to pay per hour of overtime in each department?

(20 points)

d. Suppose that 10, 6, and 8 hours of overtime may be scheduled in departments A,

B, and C respectively. The cost per hour of overtime is $17 in department A,

$21.50 in department B, and $10 in department C. Formulate a model that can be used to determine the optimal production quantity if overtime is made available. What are the optimal product quantities? What is the revised total contribution to profit? How much overtime do you recommend using in each department? What is the increase in the total contribution to profit if overtime is used?

(60 points)

Answer 1

We should use Linear Programming model to solve the problem because this a classic example of hanng a two decision variales with prof fit maximization and constraints. which have simple addtion and. multiplication which can be easily solved using simple linear programming.

Decision vanable:

Production of product 1= x

Production of product 2= y

objective function:

To maximize profrofit/ contribubon

30x +15y

Constraits:

Three main constraints of labour hours of each department.

Departmet A =1*x+0.38y<=110

Departmet B = 0.25x+ 0.3y <= 45

Departmet C = 0.25x+ 0.45y<= 60

Also, the producton of product 1 and 2 will be postive (ideally the production of products I also integers but the solver does not give-the sensitivity report with integer constrains.)

>=0

The above given linear program is solved using excel solver as shown in fig 1 and fig 2

In fig 1, the green cells are The decision variables and yellow cells are calculation for hours for each department and each product We add. The hours for each department for both products in the cells shown in red. The blue cell is The objective function of maximizing profit.

The fig2 shows The solver box, where clearly we can see the changing cells as the decision variables and. maximizing the objectve function and constrains listed as discussed above.

The optimal quantities as shown are product =77.56 = 78 units

Product2 = 85.36 = 85 units

Fig3 shows The sensitivity report for the above solver.

We can seethe labour hours for dept. A and.B has been fully utilized where as dept. C There is stii room. So, if we need to add overtime hours it should only be for dept. A &R the shadow price shown in senstivrty report shows The increase in profit per unit hour addition to the dept. for dept. A it IS 25, which means we should not pay more than $25 for overfime. Similarly we should not pay more than $17 in dept.