Use the following information to answer the questions) below. Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\ \hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\ \hline 2 & & \\ \hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\ \text { Capacity } \\ \text { mins./year) } \\ \end{array}\\ \hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\ \hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\ \hline 6 & \text { Gross margin/minute } & & & & & \\ \hline 7 & \text { Maximum production } & & & & & \\ \hline 8 & \text { Profit } & & & & & \\ \hline \end{array}$ -When a model has a unique optimal solution, it means that .

A) the objective is maximized or minimized by more than one combination of decision variables B) there is no solution that simultaneously satisfies all the constraints C) the Allowable Increase or Allowable Decrease values for changing cells are zero D) there is exactly one solution that will result in the maximum or minimum objective A) the objective is maximized or minimized by more than one combination of decision variables B) there is no solution that simultaneously satisfies all the constraints C) the Allowable Increase or Allowable Decrease values for changing cells are zero D) there is exactly one solution that will result in the maximum or minimum objective D

Use the table below to answer the following questions). Qualis Investments is a private limited business that manages personal financial portfolios. The company manages six mutual funds and has a client that has acquired $750,000 from an inheritance. Characteristics of the funds are given in the table below. $\begin{array}{|c|l|c|c|} \hline & \text { Qualis Mutual Fund Data } & & \\ \hline & & \begin{array}{c} \text { Expected Annual } \\ \text { Return } \end{array} & \text { Risk Measure } \\ \hline 1 & \text { Qualis Low-priced Stock Fund } & 7.23 \% & 11.87 \\ \hline 2 & \text { Qualis Multinational Fund } & 8.42 \% & 12.62 \\ \hline 3 & \text { Qualis Mid-cap Stock Fund } & 6.66 \% & 13.72 \\ \hline 4 & \text { Qualis Mortgage Fund } & 2.72 \% & 3.37 \\ \hline 5 & \text { Qualis Income Equity Fund } & 8.89 \% & 8.4 \\ \hline 6 & \text { Qualis Balanced Fund } & 3.50 \% & 6.91 \\ \hline \end{array}$ The company recommends that no more than $300,000 be invested in any individual fund, and that at least $80,000 be invested in each of the mid-cap stock and mortgage fund. The total amount invested in the low-priced and multinational funds are at least 35% of the total investment. The client would like an average return of at least 6%. Assume that X1- X6 represent the dollar amounts invested in funds 1 through 6, respectively. -Which of the following is the constraint for the weighted return?

A) X1 + X2 + X3 + X4 + X5 + X6 = 750,000 B) 7.23 X1 + 8.42 X2 + 6.66 .X3 + 2.72 X4 + 8.89 X5 + 3.5 X6 ? 6.00 C) 7.23 X1 + 8.42 X2 + 6.66 .X3 + 2.72 X4 + 8.89 X5 + 3.5 X6 / 750,000 ? 6.00 D) 7.23 X1 + 8.42 X2 + 6.66 .X3 + 2.72 X4 + 8.89 X5 + 3.5 X6 / 750,000 A) X1 + X2 + X3 + X4 + X5 + X6 = 750,000 B) 7.23 X1 + 8.42 X2 + 6.66 .X3 + 2.72 X4 + 8.89 X5 + 3.5 X6 ? 6.00 C) 7.23 X1 + 8.42 X2 + 6.66 .X3 + 2.72 X4 + 8.89 X5 + 3.5 X6 / 750,000 ? 6.00 D) 7.23 X1 + 8.42 X2 + 6.66 .X3 + 2.72 X4 + 8.89 X5 + 3.5 X6 / 750,000 C

Use the table below to answer the following questions). The Riviera Transport Company RTC) produces car accessories at two plants: Dallas and Atlanta. They ship them to major distribution centers in Houston, San Jose, Jacksonville, and Memphis. The accounting, production, and marketing departments have provided the information in the table below, which shows the unit cost of shipping between any plant and distribution center, plant capacities over the next planning period, and distribution center demands. RTC's supply chain manager faces the problem of determining how much to ship between each plant and distribution center to minimize the total transportation cost, not exceed available capacity, and meet customer demand. Assume Xij = amount shipped from plant i to distribution center j, where i = 1 represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on. \[\begin{array} { | l | l | l | l | l | l | } \hline \text { Transpartation } & & & & & \\ \text { Model } & & & & & \\ \hline & & & & & \\ \hline \text { Data } & & & & & \\ \hline & \text { Distribution } & & & & \\ & \text { Center } & & & & \\ \hline \text { Plant } & \text { Houston } & \text { Sarn Jose } & \text { Jacksorville } & \text { Mernphis } & \text { Capacity } \\ \hline \text { Dallas } &13.00 & 15.25 & 10.99 & 18.48 & 1250 \\ \hline \text { Atlarita } & 10.75 & 15.16 & 9.65 & 18.50 & 750 \\ \hline \text { Dernand } & 175 & 325 & 480 & 950 & \\ \hline \end{array}\] Answer the following questions) using a linear optimization model. -Keychain Publishing is planning to release two books, simultaneously, by the same author. One is a fictional book, while the other is the author's autobiography. The details of its cost, production, and demand are given in the table below. \[\begin{array}{l} \begin{array} { | l | l | l |} \hline\text { Kaychain Publishing }\\ \hline & & \\ \hline \text { Data } & & \\ \hline & \text { Fictimal } & \text { Autobiography } \\ \hline \text { Cast/book } & \$ 1.75 & \$ 1.50 \\ \hline \text { Price/book } & \$ 11.49 & \$ 9.86 \\ \hline & & \\ \hline \text { Base demand } & 50,000 & 65,000 \\ \hline \text { Increase/\$1 Adv. } & 25 & 35 \\ \hline \text { Min. percent } & & \\ \text { requirement } & 35 \% & \\ \hline \text { Max percent limitation } & 70 \% & \\ \hline & & \\ \hline \text { Total Budget } & \$ 150,000 & \\ \hline \end{array} \end{array}\] Keychain Publishing has $150,000 available to bind books and advertise them with an objective of maximizing profit contribution. Provide the objective function for maximizing profits, along with its constraints.

To formulate this model, let F = number

Use the following information to answer the questions) below. Cerebro Manufacturing produces four types of structural support fittings-plugs, rails, rivets, and clips-which are machined on two CNC machining centers. The machining centers have a capacity of 250,000 minutes per year. The gross margin per unit and machining requirements are shown in the spreadsheet below. $\begin{array}{|l|l|l|l|l|l|l|} \hline&{\text { A }} & \text { B } &C&D&E&F\\ \hline 1 & \text { Cerebro } & \\ & \text { Manufacturing Model } & \\ \hline 2 & & \\ \hline3 & \text { Product } & \text { Plugs } & \text { Rails } & \text { Rivets } & \text { Clips } &\begin{array} { l } \text { Machine } \\ \text { Capacity } \\ \text { mins./year) } \\ \end{array}\\ \hline 4 & \text { Gross margin/unit } & \$ 0.40 & \$ 1.20 & \$ 0.80 & \$ 1.10 & \\ \hline 5 & \text { Minutes/unit } & 1 & 2 & 3 & 1.5 & 250,000 \\ \hline 6 & \text { Gross margin/minute } & & & & & \\ \hline 7 & \text { Maximum production } & & & & & \\ \hline 8 & \text { Profit } & & & & & \\ \hline \end{array}$ -An infeasible problem is one for which .

A) the objective is maximized or minimized by more than one combination of decision variables B) there is no solution that simultaneously satisfies all the constraints C) the objective can be increased or decreased to infinity or negative infinity D) there is exactly one solution that will result in the maximum or minimum objective A) the objective is maximized or minimized by more than one combination of decision variables B) there is no solution that simultaneously satisfies all the constraints C) the objective can be increased or decreased to infinity or negative infinity D) there is exactly one solution that will result in the maximum or minimum objective