Instructions

$$ Submit this homework in hardcopy form at the beginning of class $($when collected$).$

$$ You must show$/$explain how you solved each problem, including equations used.

$$ Show all work. No work $=$ no credit.

$$ You must use the notation $($variable names, etc.$)$ discussed in class and in assigned readings.

$$ Follow the Homework Format $($see Canvas document from the beginning of the semester$).$

$$ This assignment should be typed and printed.

$$ To help prepare a typed homework, the document Some Formulas for Homework contains formulas that can be copied and pasted.

$$ This is an individual assignment $($working with classmates is prohibited$).$

$1)$ We sell ice cream at a retail store, which we operate $50$ weeks per year. Whenever we order from our supplier we incur a $$120$ ordering charge. Customer demand is $300$ pounds per week and it costs us $$37$ per pound per year to hold the ice cream in proper storage.

a$)$ What order size is optimal $($i$.$e$.$ what order size will minimize inventory system costs$)?$

b$)$ If we decided to use an order size of $500$ lbs $($instead of the optimal order size$),$ what would be the additional cost we would incur per year?

c$)$ We decide to make the ice cream instead of buying it$.$ We can make $1250$ pounds per week and every time we setup the ice cream making equipment it costs us $$180.$ Other information is the same as above. What is the optimal production run amount?

d$)$ In terms of relevant inventory system costs, is it more or less expensive to produce the ice cream or buy it from a supplier $($assuming we use the optimal order size or production run amount$)?$ What is the difference in the yearly total relevant cost?