Use the Table Below to Answer the Following Questions) Answer the Following Questions) Using a Linear Optimization Model

question 7

Essay

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.

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Definitions:

Quota

A government-imposed trade restriction that limits the number or monetary value of goods that can be imported or exported during a specified time period.

Revenue

The total income generated by a business or government from its activities, including sales of goods and services, taxes, and other sources.

Importer or Exporter

A business or country that buys goods from abroad (importer) or sells goods to foreign countries (exporter).

World Price

The global equilibrium price of a good or service, determined by the worldwide demand and supply.