(

a) State the utility of linear programming in business decision-making.

(

b) A toy company manufactures two types of dolls; a popular doll A and a deluxe type doll Product Machine A Machine B B. Each doll of type B takes twice as long to X

4 hours 5 hours produce one doll of type A, and the company Y

5 hours 2 hours would have time to make a maximum of 2000 dolls per day if it produced only the popular type. The supply of plastic is sufficient to produce 15,000 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 600 per day available. The company makes a profit of `3 and `5 per doll, respectively, on dolls A and B.

Formulate the linear programming problem to determine the most profitable combination of dolls A and B.