A couple sent their three children to sell 90 cookies for a charity program. The first carries 50 cookies; the middle one carries 30; and the youngest, carries only 10. The parents have stipulated five rules: (a) The selling price is either $ 1 for 7 cookies or $3 for one cookie, or a combination of the two prices, (b) Each child may exercise one or both options of the selling price, (c) Each of the three children must return with exactly the same amount of money, (d) Each child's income must be in whole dollars (no cents allowed), (e) The amount received by each child must be the largest possible. Under these stipulated conditions and given that the three kids are able to sell all they have:
a) Formulate a linear mathematical programming model for the problem to satisfy the parents conditions (clearly define your decision variables, objective and constraints).
b) Use Excel and Solver to implement and solve the model you formulated in part (a) to find the optimal solution. Report your results in the report by including a snapshot of your spreadsheet solution