Drawthe budget constraint for a consumer with standard preferences.
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1.
(i) A consumer has income of £3,000. Apple juice is priced at £3 a bottle and cheese is priced at £6 a kilo. Drawthe budget constraint for a consumer with standard preferences. What is the slope of this budget constraint?
(ii) Show a consumer’s budget constraint and indifference
(iii) The price of cheese rises from £6 to £10 a kilo, while the price of juice remains at £3 a bottle. For aconsumer with a constant income of £3,000, show what happens to consumption of juice and cheese.Decompose the change into income and substitution effects.
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- This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.An investor is considering investing in stocks, real estate, or bonds economic conditions. Suppose that the probabilities for good, stable and poor conditions are 0.2, 0.4 and … (figure it out), respectively. Table 1 shows the payoff returns for the investor’s decision situation. Table 1: Investment returns Economic Conditions Investment Good Stable Poor Stocks R5 000 R7 000 R3 000 Real estate -R2 000 R10 000 R6 000 Bonds R4 000 R4 000 R4 000 Assuming the probabilities of the occurrence of the state of nature are unknown, what will be the best investment alternative; a) If the decision maker is pessimistic about the future state, (3) b) If the decision maker strikes a compromise between the maximin and maximax, assuming the coefficient of pessimism is 0.2. (4) c) If the decision is based on opportunistic loss. (6) d) If we use the equally likelihood criterionAn investor has a certain amount of money available to invest now. Three alternative investmentsare available. The estimated profit in Kwacha of each investment under each economic conditionare indicated in the following payoff table:Event Investment SelectionA B CEconomy declines 500 -2000 -7000No charge 1000 2000 -1000Economy Expand 2000 5000 20,000Based on his own past experience, the investor assigns the following probabilities to eacheconomic condition:( )( )( )Economy declines 0.30No change 0.50Economy expands 0.20PPP===i. Determine the optimal action based on the maximax criterion ii. Determine the optimal action based on the maximin criterion iii. Compute the expected monetary value (EMV) for each investment iv. Compute the expected opportunity loss (EOL) for each investment v. Explain the meaning of the expected value of perfect information (EVPI) in thisproblem vi. Based on the results of (iii) and (iv), which investment would you choose?vii. Compute the coefficient of…
- Select the best statement if we consider the following situation: The right-hand side of a particular constraint is 30. Applying sensitivity analysis to the LP model shows that the shadow price is 1.2 and an allowable increase of 15 and allowable decrease of 10. 1.If 20≤RHS≤45, the change in the objective function value will be 1.2 times the difference between the new value and 30. 2.If 10≤RHS≤15, the change in the objective function value will be 1.2 times the difference between the new value and 30. 3.The objective function value will increase. 4.The objective function value will decrease.Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? A. Product_2 B. Product_1 C. Product_3 Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 13 5 $B$3 Product_2 175 0 25 8 9 $B$4 Product_3 0 −1.5 25 11 3 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 7002. A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal is to maximize profit, what would be the appropriate objective function? Select one: a. Maximize profit Z = $10Y + $25Z b. Maximize profit Z = 0.25Y + 0.20Z c. Maximize profit Z = $40Y + $25Z d. Maximize profit Z = $50(Y + Z) e. Maximize profit Z = $30Y + $20Z
- Alexis Harrington received an inheritance of $95,000, and she is considering two speculative investmentsthe purchase of land and the purchase ofcattle. Each investment would be for 1 year. Under the present (normal) economic conditions, each dollar invested in land will return the principalplus 20% of the principal; each dollar invested in cattle will return the principal plus 30%. However, both investments are relatively risky. If economic conditions were to deteriorate, there is an 18% chance she would lose everything she invested in land and a 30% chance she would loseeverything she invested in cattle. Alexis does not want to lose more than $20,000 (on average). She wants to know how much to invest in eachalternative to maximize the cash value of the investments at the end of 1 year Should all of Alexis's inheritance be invested according to the optimal solution?Alexis Harrington received an inheritance of $95,000, and she is considering two speculative investmentsthe purchase of land and the purchase ofcattle. Each investment would be for 1 year. Under the present (normal) economic conditions, each dollar invested in land will return the principalplus 20% of the principal; each dollar invested in cattle will return the principal plus 30%. However, both investments are relatively risky. If economic conditions were to deteriorate, there is an 18% chance she would lose everything she invested in land and a 30% chance she would loseeverything she invested in cattle. Alexis does not want to lose more than $20,000 (on average). She wants to know how much to invest in eachalternative to maximize the cash value of the investments at the end of 1 year How much "profit" would the optimal solution earn Alexis over and above her investment?In the problem on excel : 1.What are the decision variables 2.What is the objective functions 3. What are the constraints and explain A used t company, owned by Musa in Ottawa sells 7 different brands covering 3 different products. These are 4 Brands of Cars: Toyota, Honda, Chevrolet and BMW; 2 brands of Motorcycles: Suzuki and Yamaha, and 1 brand of Sailboats: Amel. Musa knows that his sales floor which he will display his products is 70,000 square feet, and that a Car takes 60 square feet of space, a motorcycle takes 20 square feet of space, and a sailboat takes 800 square feet of space. The profit that can be made for selling each of 7 different items is listed below: ITem Profit per unit Car - Toyota $2800 Car - Honda $3900 Car - Chevrolet $2,100 Car - BMW $5000 Motorcycle - Suzuki $1,000 Motorcycle - Yamaha $2,250 Sailboat - Amel $9,500 The transportation company is trying to determine how many of each item to order to maximize profit, given the following restrictions: 1.…
- Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 10 5 $B$3 Product_2 175 0 25 10 14 $B$4 Product_3 0 −1.5 25 8 6 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 Choose the product Product 1 Product 2 Product 3Only Construct Linear Programming Model for the following Problemb; An individual wishes to invest $9000 over the next year in two typar of inventrent linvestment A yinlds 5% and invertment � yields 8%. Market retearch rocotnenends an allocs tion of at least 25% in A and at most 30% in �. Motsover, investment in A should be at least ball the invertmeut in �. How should the fund be allocated to the two imetrinents?A decision problem has the following three constraints: 70X + 6Y <= 420; 24X + 3Y= 72; and 11X - Y <= 14 . The objective function is Min 17X + 38Y . The objective function value is : a. 338 b. 676 c. unbounded d. infeasible e. 0