10. Two alloys, A and B, are made from fOUf metals, I, II, III, and IV, according to the following specifications:

Alloy A

B Specifications At most 80% of I At most 30% of II At least 50% of IV Between 40% and 60% of II At least 30% of III At most 70% of IV Selling price ($)

200 300 The fOUf metals, in turn, are extracted from three ores according to the following data:

Constituents (%)

Maximum quantity Ore (tons) I If 1lI IV Others Price/ton ($)

1 1000 20 ]0 30 30 10 30 2 2000 10 20 30 30 10 40 3 3000 5 5 70 20 0 50 How much of each type of alloy should be produced? (Hint: Let Xkj be tons of are i allocated to alloy k, and define Wk as tons of alloy k produced.)