Homework Problem Set #1
Delectation Delicatessen
Problem a)
Answer:
Delectation wants to determine the number of Fish-n-Fowl and Surf-n-Turf sandwiches it should make each day to maximize the deli’s revenues in USD$. The decision variables are how many units of Fish-n-Fowl and Surf-n-Turf sandwiches Delectation should make each day.
F= units of Fish-n-Fowl sandwiches Delectation should make each day. S= units of Surf-n-Turf sandwiches Delectation should make each day.
The objective function: maxmize F x 5.50 + S x 6.95
The Constraints: 0.25 x F + 0.25 x S<=200 | Tuna fish salad | Pound | 0.5 x F <=260 | Sliced turkey | Pound | 0.40 x S <=60 | Sliced roast beef…show more content… So Gaussian should take the order.
Problem d)
Answer:
The 800 units production line should be added to plant C .The reasons are: 1. Plant C has the higher absolute value of shadow price. One addition unit of production can reduce costs by $0.75. 2. 800 units are within the allowable increase for Plan C. So adding 800 units on Plant will cause costs savings of 800 x $0.75. 3. Total costs savings from adding small line are $0.75x500-$400= -$25<0
Total costs savings from adding large line are $0.75 x 800-$500= $100>0
So adding large line is more financial beneficial.
National steel company
Problem a) losing 100 units of production capacity at plant A
Answer:
Variables
P1, P2, P3, P4 as production in Jan, Feb, Mar and Apr
I1, I2, I3, I4 as ending inventory of Jan, Feb, Mar and Apr
U1, U2, U3, U4 as the increase of product in Jan, Feb, Mar and Apr
D1, D2, D3, D4 as the decrease of product in Jan, Feb, Mar and Apr
The objective function: minimize total costs consist of the following 3
Minimize P1x3000+P2x3300+P3x3600+P4x3600+(300+2xI1+2xI2+2xI3+I4) x 255/2+ (U1+U2+U3+U4)x110+(D1+D2+D3+D4)x90
1. Production costs: P1x3000+P2x3300+P3x3600+P4x3600
2. Inventory cost based on average inventory: (300+2xI1+2xI2+2xI3+I4) x 255/2
3. Hiring and firing cost: (U1+U2+U3+U4)x110+(D1+D2+D3+D4)x90
The objective
