Byron's Manufacturing makes tables. Demand for the next four months and capacities of the plant are shown in the table below. Unit cost on regular time is $40. Overtime cost is 150% of regular time cost

Subcontracting is available in substantial quantity at $75 per unit. Holding costs are $5 per table per month; back orders cost the firm $10 per unit per month. Byron's management believes that the transportation algorithm can be used to optimize this scheduling problem. The firm has 50 units of beginning inventory and anticipates no ending inventory.

March April May June
Demand 400 600 600 700
Regular capacity 400 400 400 400
Overtime capacity 100 100 100 100
Subcontract cap. 150 50 50 50

Answer the following questions based on the data table and solution table shown below.

Byron's Manufacturing
March April May June SUPPLY
Beginning Inventory 0 5 10 15 50
March regular time 40 45 50 55 400
March overtime 60 65 70 75 100
March subcontracting 75 80 85 90 150
April regular time 50 40 45 50 400
April overtime 70 60 65 70 100
April subcontracting 85 75 80 85 50
May regular time 60 50 40 45 400
May overtime 80 70 60 65 100
May subcontracting 95 85 75 80 50
June regular time 70 60 50 40 400
June overtime 90 80 70 60 100
June subcontracting 105 90 85 75 50
DEMAND 400 600 600 700

Byron's Manufacturing Solution
Optimal Cost =
$109,750 March April May June DUMMY
Beginning Inventory 50.
March regular time 350. 50.
March overtime 100.
March subcontracting 100. 50.
April regular time 400.
April overtime 50. 50.
April subcontracting 50.
May regular time 400.
May overtime 50. 50.
May subcontracting 50. 50.
June regular time 400.
June overtime 100.
June subcontracting 50. 100.

a. How many units will be produced on regular time in June?
b. How many units will be produced by subcontracting over the four-month period?
c. What will be the inventory at the end of April?
d. What will be total production from all sources in April?
e. What will be the total cost of the optimum solution?
f. Does the firm utilize the expensive options of subcontracting and back ordering? When; why?

(a) 400; (b) 250; (c) 0; (d) 550; (e) Total Cost = $109,750; (f) The firm uses subcontracting, but not backordering; there is no production in one month for "delivery" in an earlier month. Subcontracted quantities are 100 in March, 50 each in April, May, and June.