George johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. the trust fund has two investment options: (1) a bond fund and (2) a stock fund. the projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. whatever portion of the inheritance george finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund. in addition, he wants to select a mix that will enable him to obtain a total return of at least 7.5%. formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. if required, round your answers to three decimal places. value of optimal solution is %

$527.7.if the following was the question  $527.7 is the answer.students who are trying to raise funds have an agreement with a local pizza chain. the chain has agreed to sell them pizzas at a discount, which the students can then resell to families in the local community for a profit. it is expected that of the 500 families in the community, at most 70% will buy pizza. based on a survey of their personal preferences, the students believe that they should order no more than 120 cheese pizzas, no more than 150 pepperoni pizzas, and no more than 100 vegetarian pizzas. they also want to make sure that at least 20% of the total pizzas are cheese and at least 50% of the pizzas are pepperoni. they make a profit of $1.45, $1.75, and $1.98, respectively, for each cheese, pepperoni, and vegetarian pizza they resell. how many pizzas of each type should they buy?