Please do all 5 parts of this R coding question quick. Thanks.
Mrs. Spronners is a family-owned soap manufacturer that produces a popular line of premium liquid soaps in various flavors, including citrus, almond, lavender, and peppermint. Each year, the company releases a special seasonal variation: a green tea scented soap, which is manufactured and sold for a limited time only. The fixed cost to produce the year's batch of green tea soap is $175,000. The variable cost per unit, which includes raw materials, manufacturing, and selling costs, is $7.50 per bottle. Like many companies, Mrs. Spronners sells its products at wholesale prices to distributors, who then sell the product to retail stores at a marked-up price. Traditionally, the company prefers to focus its efforts on sales in certain American markets, where the seasonal release has proven reliably popular even when sold at premium prices. American distributors will purchase the product at a fixed price of $12 per bottle. In the event that the company overproduces, all surplus units will be sold to a single overseas distributor, where it is sold for a lesser price. The overseas distributor has agreed to pay a fixed salvage price of $8.50 per bottle. Due to current unfavorable economic conditions, demand for the coming year is unusually uncertain. Forecasts project expected sales of 90,000 bottles with a standard deviation of 40,000 bottles. The normal distribution is assumed to be a good description of annual demand. Management has tentatively decided to produce 90,000 units (to match forecasted demand) but wants to conduct an analysis regarding this production quantity before finalizing its decision. a. Write the equation that models the company's net profit for a batch of green tea soap. In this equation, express profit, demand, and supply as random variables. Note: In this case, revenue must be further decomposed into two parts: revenue from sales and revenue from salvage (leftover product). The salvage quantity can be expressed as the excess of supply over demand. b. In R, create a set of 1 million simulations of the annual demand for the green tea soap. Write the commands necessary to simulate demand and adjust the simulations to a) reflect integer values only, b) have a minimum value of 0 units, and c) have a maximum value equal to the supply quantity. Use a seed value of 30. c. In R, create a vector of simulated salvage values, using demand simulations generated in part (b) and the fixed supply quantity. d. In R, create a set of simulations of annual net profit for this product, using the profit equation created in part (a), your demand simulations from part (b), and your salvage simulations from part (c). What is the average net profit observed in your simulations? e. According to your simulations, what is the probability of earning of profit at all under these conditions? Write the R command and your answer. Mrs. Spronners is a family-owned soap manufacturer that produces a popular line of premium liquid soaps in various flavors, including citrus, almond, lavender, and peppermint. Each year, the company releases a special seasonal variation: a green tea scented soap, which is manufactured and sold for a limited time only. The fixed cost to produce the year's batch of green tea soap is $175,000. The variable cost per unit, which includes raw materials, manufacturing, and selling costs, is $7.50 per bottle. Like many companies, Mrs. Spronners sells its products at wholesale prices to distributors, who then sell the product to retail stores at a marked-up price. Traditionally, the company prefers to focus its efforts on sales in certain American markets, where the seasonal release has proven reliably popular even when sold at premium prices. American distributors will purchase the product at a fixed price of $12 per bottle. In the event that the company overproduces, all surplus units will be sold to a single overseas distributor, where it is sold for a lesser price. The overseas distributor has agreed to pay a fixed salvage price of $8.50 per bottle. Due to current unfavorable economic conditions, demand for the coming year is unusually uncertain. Forecasts project expected sales of 90,000 bottles with a standard deviation of 40,000 bottles. The normal distribution is assumed to be a good description of annual demand. Management has tentatively decided to produce 90,000 units (to match forecasted demand) but wants to conduct an analysis regarding this production quantity before finalizing its decision. a. Write the equation that models the company's net profit for a batch of green tea soap. In this equation, express profit, demand, and supply as random variables. Note: In this case, revenue must be further decomposed into two parts: revenue from sales and revenue from salvage (leftover product). The salvage quantity can be expressed as the excess of supply over demand. b. In R, create a set of 1 million simulations of the annual demand for the green tea soap. Write the commands necessary to simulate demand and adjust the simulations to a) reflect integer values only, b) have a minimum value of 0 units, and c) have a maximum value equal to the supply quantity. Use a seed value of 30. c. In R, create a vector of simulated salvage values, using demand simulations generated in part (b) and the fixed supply quantity. d. In R, create a set of simulations of annual net profit for this product, using the profit equation created in part (a), your demand simulations from part (b), and your salvage simulations from part (c). What is the average net profit observed in your simulations? e. According to your simulations, what is the probability of earning of profit at all under these conditions? Write the R command and your
