Question

p p please write each step out clearly

3. A manager of a company is considering four alternatives in which to invest additional funds: product research, product development, manufacturing operations improvements and sales promotion. The company has $1,850,000 available for this investment. The return for sales promotion is 12% per year. The return for manufacturing operations improvements is 9% per year. The return for product research is 9% per year and the return for product development is 8% per year. To diversify the investment, the manager wants to include the requirements that at least $600,000 in sales promotion, at least $200,000 in manufacturing operations improvements, at least $150,000 in product research and at least $100,000 in product development must be invested. The money invested in product research cannot be more than the money invested in manufacturing operations improvements. She wants to know how much should be invested in each of the four alternatives to maximize the total annual return. Formulate a linear programming model for the above situation by determining (a) The decision variables (b) The objective function. What does it represent? (c) All the constraints. Briefly describe what each constraint represents. Note: Do NOT solve the problem after formulating.

Answer 1

It is assumed that a, b, c and d is the fund which is allocated for each of the following

a= product research

b=product development

c=manufacturing operations improvements

d=sales promotion

Since the total annual return is to be maximised, the objective function will be

Max [0.12d+0.09c+0.09a+0.08b]

Subject to

a+b+c+d <=1850000

d=>600000,

c=>200000

a=>150000

b=>100000

a<=c

or a-c<=0

a=>0, b=>0,c=>0, d=>0