Exam 9: Linear Programming Applications

Information on a prospective investment for Wells Financial Services is given below. In each period,funds available for investment come from two sources: loan funds and income from the previous period's investment.Expenses,or cash outflows,in each period must include repayment of the previous period's loan plus 8.5% interest,and the current payroll payment.In addition,to end the planning horizon,investment income from period 4 (at 110% of the investment)must be sufficient to cover the loan plus interest from period 4.The difference in these two quantities represents net income,and is to be maximized.How much should be borrowed and how much should be invested each period?

BP Cola must decide how much money to allocate for new soda and traditional soda advertising over the coming year.The advertising budget is $10,000,000.Because BP wants to push its new sodas,at least one-half of the advertising budget is to be devoted to new soda advertising.However,at least $2,000,000 is to be spent on its traditional sodas.BP estimates that each dollar spent on traditional sodas will translate into 100 cans sold,whereas,because of the harder sell needed for new products,each dollar spent on new sodas will translate into 50 cans sold. To attract new customers BP has lowered its profit margin on new sodas to 2 cents per can as compared to 4 cents per can for traditional sodas.How should BP allocate its advertising budget if it wants to maximize its profits while selling at least 750 million cans?