Q$1-$ In $2017,$ the Restaurant Hospitality website reported that only $11\%$ of surplus food is being recovered in the food service and restaurant sector, leaving approximately $1\mathrm{.}5$ billion meals per year uneaten. Assume that this is the true population proportion and that you plan to take a sample survey of $525$ companies in the food service and restaurant sector to further investigate their behavior. You suspect that restaurants are doing a far better job in recovering surplus food than what has been reported by the website.

Suppose that based on the sample you collected restaurants report an average of $59$ surplus meals per day of which an equivalent of $51$ meals is thrown away. Respond to the following questions:$$

a$.$ Set up the research question and hypotheses.

b$.$ Calculate the p$-$value using the $$Norm$.$dist$$ Excel command.

c$.$ What is your conclusion?$$

Q$2-$ A computer manufacturer needs $7,500$ units of a component to complete an order for a distributor. If done in$-$house, the fixed cost would be$$325,000$ with variable cost at $$25$ per unit. Alternative two is to outsource for a total cost of $$75$ per unit with a set$-$up$/$tooling cost of $$50,000($fixed cost$).$ The selling price for the item is $$110.$ Answer the following questions:

a$.$ Determine the breakeven quantity for each alternative.

b$.$ Determine the breakeven quantity between the two alternatives. In other words, at what level of production the company would be indifferent between outsourcing the order and in$-$house production.

c$.$ For the current order, should they make the item in$-$house or outsource it$?$

d$.$ At what order quantity would it become optimal to make the item in$-$house rather than outsourcing it$?$