Two Factor Opportunity Set

 
two factors of productionLABOR and CAPITAL
two productsBREAD and CLOTH
two technologiesBAKING and WEAVING
Note that for each product, there is only one technology,  and both require the input of both factors of production. The technologies are assumed to be 'fixed coefficients',  i.e. requiring the constant quantity of input per each unit of output.
Notation:

 

variablesparameters
quantitiesunits:technical coefficients:units:
L  ... LABORman-hoursb ...LABOR - BREADhours per  one loaf
K ... CAPITALpiecesc ... LABOR - CLOTHhours per one yard
QB... BREADloavesd ...CAPITAL - BREADpieces per  one loaf
QC...CLOTHyardse ... CAPITAL - CLOTHpieces per one yard
Equations:

 

(1)LB  =   b QBLABOR needed for BAKING QB loaves of BREAD.
(2)LC   =   c QCLABOR needed for WEAVING QC yards of CLOTH.
(3)L >=  LB  +  LC
Sum of LABOR needed for BAKING and WEAVING
cannot exceed available man-hours of LABOR.
(4)KB  =   d QBCAPITAL needed for BAKING QB loaves of BREAD.
(5)KC   =   e QCCAPITAL  needed for WEAVING QC yards of CLOTH.
(6)K >=  KB  +  KC
Sum of CAPITAL needed for BAKING and WEAVING
cannot exceed available pieces of CAPITAL.