Agricultural Studies 3300
Agricultural Systems Modeling I
Fall 2008
Assignment # 10
Due Friday, December 5th , 2008, At 8am.
PRIMAL:
A carpenter produces tables (X1) and chairs (X2) for sale in a market. He makes a net income
of $50 of each table and $30 off each chair. Production times required for a table and a chair are
measured at different times of day, and estimated to be 2 hours and 1 hour, respectively. Total
labor hours per week available are only 40 hrs. Raw materials required for a table and a chair are
1, and 2 units respectively. Total supply of raw material is 50 units per week.
Formulate the problem and solve using excel. Interpret all shadow prices and reduced costs.
What hourly wage would the carpenter be willing to pay his neighbor to help him out?
DUAL:
Suppose the Carpenter wishes to buy insurance for his net income. Let U1 = the dollar amount
payable to the Carpenter for every labor hour lost (due to illness, for example), and U2 = the
dollar amount payable to the Carpenter for every raw material unit lost (due to fire, for example).
The insurance officer tries to minimize the total amount of $(40U1 + 50U2) payable to the
Carpenter by the insurance company. However, the Carpenter will set the constraints (i.e.
conditions) by insisting that the insurance company cover all his/her loss that is his net income
since he/she cannot make the products. Formulate this problem as the dual to the original
problem. Interpret all shadow prices and reduced costs.