Could you answer these questions, in a powerpoint Question 3Fox Studios is a pest rabbit control company commissioned to assist with a wild rabbit populationgrowth problem on a small island.1000 rabbits were introduced onto an island, but it was soon realised that the population growth ofthe rabbits would cause environmental problems on the island. Fox Studios was commissioned toassist with this problem by introducing foxes who help contain the rabbit numbers.The rabbit population growth rate is 10% each month, (This is the net of the natural birth rate anddeath rate).Each fox eats 10 rabbits per month. (The foxes are also fed by the company as part of their cost).(a) Show that R₁+1 = 1.1 R₁ - 10 F where R, is the rabbit population at month t and F isthe number of foxes employed, is a suitable difference equation to use.(b) Verify that R = (1000 - 100 F) × 1.1⁰ + 100 F is the solution to the differenceequation.(c) Fox Studios is faced with the following optimisation problem:i. The contract is for 5 years (60 months)ii.Each fox costs $300 000 (special training, transportation, feeding andmedical expenses over the 5 years)iii.The company is liable to pay a fine of $1 per rabbit for any excess over15 000 in every month during the 5 year life.Solve for the number of foxes that should be sent to minimise the cost to the company.Hints:i.ii.iii.There are 11 cases to consider F=0, 1, 2, ... 10R is an increasing function in t with a calculable time of first breach say T*.An EXCEL spread sheet may be used, but theoretical calculations should be performed. Question 1A boutique fruit juice manufacturer produces 2 types of juices, Apple and Fig daily with a total costfunction: TC = 6A + AxF+9Fwhere:A is the quantity of the Apple juice (in kegs) andF is the quantity of the Fig juice (in kegs).The prices that can be charged are determined by supply and demand forces and are influenced bythe quantities of each type of juice according to the following equations:P₁ = 17-A + F for the price (in dollars per keg) of the Apple juice andPF = 23 + 2A-F for the price (in dollars per keg) of the Fig juice.The total revenue is given by the equation:TR = PAX A+ PF XFand the profit given by the equationProfit= TR-TCFirst, use a substitution of the price variables to express the profit in terms of A and F only.Using the method of Lagrange Multipliers find the maximum profit when total production (quantity)is restricted to 2023 kegs. Note A or F need not be whole numbers.Be sure to show that your solution is a maximum point.

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A boutique fruit juice manufacturer produces 2 types of juices, Apple and Fig daily with a total cost function: TC = 6A+AxF+9F where: A is the quantity of the Apple juice (in kegs) and F is the quantity of the Fig juice (in kegs).

A boutique fruit juice manufacturer produces 2 types of juices, Apple and Fig daily with a total cost function: TC = 6A+AxF+9F where: A is the quantity of the Apple juice (in kegs) and F is the quantity of the Fig juice (in kegs).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.3P

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Question 1 A boutique fruit juice manufacturer produces 2 types of juices, Apple and Fig daily with a total cost function: TC = 6A + A × F +9F where: A is the quantity of the Apple juice (in kegs) and F is the quantity of the Fig juice (in kegs). The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type of juice according to the following equations: P₁ = 17-A + F for the price (in dollars per keg) of the Apple juice and PF = 23+2A-F for the price (in dollars per keg) of the Fig juice. The total revenue is given by the equation: TR = PAXA + PF XF and the profit given by the equation Profit = TR - TC First, use a substitution of the price variables to express the profit in terms of A and F only. Using the method of Lagrange Multipliers find the maximum profit when total production (quantity) is restricted to 2023 kegs. Note A or F need not be whole numbers. Be sure to show that your solution is a maximum point.
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