A small firm makes three similar products which all follow t

A small firm makes three similar products, which all follow the same threestep process, consisting of milling, inspection, and drilling. Product A requires 12 minutes of milling, 5 minutes for inspection, and 10 minutes of drilling per unit; product B requires 10 minutes of milling, 4 minutes for inspection, and 8 minutes of drilling per unit; product C requires 8 minutes of milling, 4 minutes for inspection, and 16 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $2.4 per unit to profit, product B contributes $2.5 per unit, and product C contributes $3.0 per unit. Determine the optimal mix of products in terms of maximizing contribution to profits for the period.

c) What is the optimal solution?

d) What is the optimal objective function value?

e) Do any of the constraints have any slack? If yes, which ones?

Solution

            X         Y         Z                     RHS    Dual

Maximize        2.4       2.5       3                                

Milling 12        10        8          <=        20        .1667

Inspection       5          4          4          <=        15        0

Drilling            10        8          16        <=        24        .1042

Solution->       0          1.3333 .8333               5.8333

Variable               Status   Value

X             NONBasic            0

Y              Basic      1.3333

Z              Basic      .8333

slack 1   NONBasic            0

slack 2   Basic      6.3333

slack 3   NONBasic            0

Optimal Value (Z)                             5.8333

c) the optimal solution X=0, Y= 1.3333, Z =.8333

d) the optimal objective function value P= 5.8333

e) Do any of the constraints have any slack- Yes

If yes, which ones. Inspection