Show me the steps to solve Supply Contracts

Answer the following questions. Provide answers in a $.$docx file and show screen captures if you used a software tool $($such as Excel$).$ Upload supporting files. You may use the Excel examples provided in the lesson.

A publisher sells books to Barnes & Noble at $$12$ each. The marginal production cost for the publisher is $$1$ per book. Barnes & Noble prices the book to its customers at $$24$ and expects demand over the next two months to be normally distributed, with a mean of $20,000$ and a standard deviation of $5,000.$ Barnes & Noble places a single order with the publisher for delivery at the beginning of the two$-$month period. Currently, Barnes & Noble discounts any unsold books at the end of two months down to $$3,$ and any books that did not sell at full price sell at this price.

How many books should Barnes & Noble order? What is its expected profit? How many books does it expect to sell at a discount?

What is the profit that the publisher makes, given Barnes & Noble$$s actions?

A plan under discussion is for the publisher to refund Barnes & Noble $$5$ per book that does not sell during the two$-$month period. As before, Barnes & Noble will discount them to $$3$ and sell any that remains. Under this plan, how many books will Barnes & Noble order? What is the expected profit for Barnes & Noble? How many books are expected to be unsold? What is the expected profit for the publisher? What should the publisher do$?$

Topgun Records and several movie studios have decided to sign a revenue$-$sharing contract for CDs$.$ Each CD costs the studio $$2$ to produce. The CD will be sold to Topgun for $$3.$ Topgun, in turn, prices a CD at $$15$ and forecasts demand to be normally distributed, with a mean of $5,000$ and a standard deviation of $2,000.$ Any unsold CDs are discounted to $$1,$ and all sell at this price. Topgun will share $35$ percent of the revenue with the studio, keeping $65$ percent for itself.

How many CDs should Topgun order?

How many CDs does Topgun expect to sell at a discount?

What is the profit that Topgun expects to make?

What is the profit that the studio expects to make?

Repeat parts $($a$)($d$)$ if the studio sells the CD for $$2($instead of $$3)$ but gets $43$ percent of revenue.

Benetton has entered into a quantity flexibility contract with a retailer for a seasonal product. If the retailer orders O units, Benetton is willing to provide up to another $35$ percent if needed. Benetton$$s production cost is $$20,$ and it charges the retailer a wholesale price of $$36.$ The retailer prices to customers at $$55$ per unit. Any unsold units can be sold by the retailer at a salvage value of $$25.$ Benetton can salvage only $$10$ per unit for its leftover inventory. The retailer forecasts demand to be normally distributed, with a mean of $4,000$ and a standard deviation of $1,600.$

How many units O should the retailer order?

What is the expected quantity purchased by the retailer $($recall that the retailer can increase the order by up to $35$ percent after observing demand$)?$

What is the expected quantity sold by the retailer?

What is the expected overstock at the retailer?

What is the expected profit for the retailer?

What is the expected profit for Benetton?

Consider a manufacturer selling DVDs to a retailer for $$6$ per DVD$.$ The production cost of each DVD is $$1$ and the retailer prices each DVD at $$10.$ Retail demand for DVDs is normally distributed, with a mean of $1,000$ and standard deviation of $300.$ The manufacturer has offered the retailer a quantity flexibility contract with $\backslash$alpha $=\backslash$beta $=0\mathrm{.}2.$ The retailer places an order for $1,000$ units. Assume that salvage value is zero for both the retailer and the manufacturer.

What is the expected profit for the retailer and manufacturer?

How much will profit increase for the retailer if $\backslash$alpha increases to $0\mathrm{.}5?$

How much will profit increase for the retailer if $\backslash$beta increases to $0\mathrm{.}5($keeping $\backslash$alpha at $0\mathrm{.}2)?$

$[$Note: All of the above questions have a normally distributed demand. But, in some cases, demand is not distributed normally and demand forecasts have a discrete probability distribution. You may refer the Simchi$-$Levi example Excel file for sample application of supply contracts and cost$-$sharing contracts.$]$

A manufacturer of a seasonal product $($such as Christmas trees$)$ has a demand forecast as given below:

Demand $20002100220023002400250026002700$

Probability $3\%8\%15\%30\%17\%12\%10\%5\%$

This means, the probability of demand being $2200$ units $=$ P $($Demand $=2200)15\%.$

The probability of demand being $2200=$ P $($Demand $<=2200)=3\%+8\%+15\%=26\%$

Suppose the unit production cost is $$20/$ unit. The distributor sells to end customers for $$50/$unit during season and sells any unsold units for $$10/$unit after season.

What is the system optimal production quantity and expected profit under global optimization? $($This means, the manufacturer and the distributor are one organization.$)$

Suppose the manufacturer is make$-$to$-$order;