Worksheet Week $2$

Math $112,$ Fall $2023$

A particular toy has become more popular then expected during the holiday season and the company who produces it needs to increase its production levels in December. Most years the production schedule demands that they've produced $p(t)$ total toys $t$ days after December $1$st$.$

$($a$)$ One suggestion is that they produce an extra $500$ toys in November so that their expected production level is always $500$ toys higher then normal. Find a function $q$ which reflects this plan.

$($b$)$ Another suggestion is that they demand $40\%$ higher production levels throughout the entire moth. Find a function $R$ which reflects this plan.

$($c$)$ A third suggestion is that they get an early jump on production the December supply by moving the schedule up $15$ days. Find a function $q$ which reflects this plan.

$($d$)$ The complain actually decides to go with a production plan where they aim to produce a total of $p(\frac{t}{2})$ toys $t$ days after December $1$st$.$ Explain how this new plan compares with the usual plan.

$1$