Your local Book Store is planning on buying four new educational book titles for its repository. For this purpose, the Book Store has contacted the publishers of the four books and received the following price quotes: - Purchase cost of book 1 per unit: $5 - Purchase cost of book 2 per unit: $7 - Purchase cost of book 3 per unit: $6 - Purchase cost of book 4 per unit: $4 The Book Store has also estimated the revenue from selling the books will be as follows: - Revenue from selling book 1 per unit: $17 - Revenue from selling book 2 per unit: $18 - Revenue from selling book 3 per unit: $16 - Revenue from selling book 4 per unit: $19 The Book Store is predicting that by the end of the year the overall demand for book 1 and book 2 will be 100 books and the overall demand for book 3 and book 4 will be 125 books. The publishers of book 1 and book 2 also offer online supplementary content that cost $2 for book 1 and $3 for book 2 . The overall budget allocated for buying book 1 and book 2 is $750, and for their online supplementary content, there is an additional $500 set aside. There are no budget limits for book 3 and book 4. Also, the supplementary content of book 1 and book 2 will be offered to the customers for free. The Book Store is aiming at maximizing its profit from selling the books by finding the optimal number of each of the four books to order. a) Formulate the linear programming (LP) model for Book Store. Show all workings and steps for model formulation. (5 marks) Figure 1 shows how the Book Store analyst prepared the excel file for LP problem: Below is Figure 2 that shows how the Book Store analyst has solved the LP problem: Canctrainte b) Using Figure 1, indicate which cell numbers are denoting objective function, decision variables, LHS of all constraints. For example: cell number D21, D22, D23, D24 denote RHS of all constraints about overall demand 1 , overall demand 2, overall budget 1 , and overall budget 2 . (1 mark) c) For the optimal solution, how many of the book titles are purchased and what is the maximum profit? (2 mark) d) For the optimal solution, how much of the budget for purchasing book 1 and book 2 is left? (2 marks) e) How much more profit will Book Store earn if they increase their demand for book 3 and book 4 by 20% ? (2 marks) f) What would be the optimal solution if Book Store received a discount of $3 on book 1 's purchase price? (3 marks) g) What is the maximum quantity of demand of book 1 and book 2 that Book Store can satisfy without any changes in the shadow price? (2 marks) h) How much more budget should Book Store allocate for book 1 and book 2 to increase its profit? (3 marks) (ii) (5 marks) A bank in Dammam is deciding on how to design its next year's ad campaigns for a new banking product and can spend its budget on buying spots in internet platforms, local TV, and print media. Information about each medium is shown below. The number of internet platform spots cannot exceed the number of TV spots by more than 5 . The advertising budget of the bank is $15,000. Using the multi-step model formulation approach, formulate the model that will maximize the audience reached and achieve a media quality of at least 2000 . Show all workings and steps for model formulation. You do not need to solve the model. Your local Book Store is planning on buying four new educational book titles for its repository. For this purpose, the Book Store has contacted the publishers of the four books and received the following price quotes: - Purchase cost of book 1 per unit: $5 - Purchase cost of book 2 per unit: $7 - Purchase cost of book 3 per unit: $6 - Purchase cost of book 4 per unit: $4 The Book Store has also estimated the revenue from selling the books will be as follows: - Revenue from selling book 1 per unit: $17 - Revenue from selling book 2 per unit: $18 - Revenue from selling book 3 per unit: $16 - Revenue from selling book 4 per unit: $19 The Book Store is predicting that by the end of the year the overall demand for book 1 and book 2 will be 100 books and the overall demand for book 3 and book 4 will be 125 books. The publishers of book 1 and book 2 also offer online supplementary content that cost $2 for book 1 and $3 for book 2 . The overall budget allocated for buying book 1 and book 2 is $750, and for their online supplementary content, there is an additional $500 set aside. There are no budget limits for book 3 and book 4. Also, the supplementary content of book 1 and book 2 will be offered to the customers for free. The Book Store is aiming at maximizing its profit from selling the books by finding the optimal number of each of the four books to order. a) Formulate the linear programming (LP) model for Book Store. Show all workings and steps for model formulation. (5 marks) Figure 1 shows how the Book Store analyst prepared the excel file for LP problem: Below is Figure 2 that shows how the Book Store analyst has solved the LP problem: Canctrainte b) Using Figure 1, indicate which cell numbers are denoting objective function, decision variables, LHS of all constraints. For example: cell number D21, D22, D23, D24 denote RHS of all constraints about overall demand 1 , overall demand 2, overall budget 1 , and overall budget 2 . (1 mark) c) For the optimal solution, how many of the book titles are purchased and what is the maximum profit? (2 mark) d) For the optimal solution, how much of the budget for purchasing book 1 and book 2 is left? (2 marks) e) How much more profit will Book Store earn if they increase their demand for book 3 and book 4 by 20% ? (2 marks) f) What would be the optimal solution if Book Store received a discount of $3 on book 1 's purchase price? (3 marks) g) What is the maximum quantity of demand of book 1 and book 2 that Book Store can satisfy without any changes in the shadow price? (2 marks) h) How much more budget should Book Store allocate for book 1 and book 2 to increase its profit? (3 marks) (ii) (5 marks) A bank in Dammam is deciding on how to design its next year's ad campaigns for a new banking product and can spend its budget on buying spots in internet platforms, local TV, and print media. Information about each medium is shown below. The number of internet platform spots cannot exceed the number of TV spots by more than 5 . The advertising budget of the bank is $15,000. Using the multi-step model formulation approach, formulate the model that will maximize the audience reached and achieve a media quality of at least 2000 . Show all workings and steps for model formulation. You do not need to solve the model
