A company sells doughnuts. They incur a fixed cost of $$\sage {fixedCost1}$ for rent, insurance, and other expenses. It costs $$\sage {productionCost1}$ to produce each doughnut. The company sells each doughnut for $$\sage {sellingPoint1}$.

Part A. Construct a linear model that describes their total costs, $C$, as a function of the number of doughnuts, $x$, they produce.

$C(x) = \answer {\sage {costs1}}$

Part B. Construct a linear model that describes their total profits, $P$, as a function of the number of doughnuts, $x$, they produce.

$P(x) = \answer {\sage {profits1}}$

Part C. Construct a linear model that describes their total revenue, $R$, as a function of the number of doughnuts, $x$, they produce.

$R(x) = \answer {\sage {revenue1}}$

Aubrey is a college student going into her first year at UF. She will receive Bright Futures, which covers her tuition plus a $300 educational expense each Fall and Spring semester. Before college, Aubrey saved up $\$\sage {savings2}$. She knows she will need to pay $\$\sage {rent2}$ in rent a month, $\$\sage {food2}$ for food a week, and $\$\sage {misc2}$ in other weekly expenses.

Part A. Construct a linear model that describes her total costs, $C$ as a function of the number of months, $x$, she is at UF during Fall semester.

$C(x) = \answer {\sage {costs2}}$

Part B. Construct a linear model that describes her total income, $I$, as a function of the number of months, $x$, she is at UF during Fall semester.

$I(x) = \answer {\sage {profits2}}$

Part C. Construct a linear model that describes their total budget, $B$, as a function of the number of months, $x$, she is at UF during Fall semester.

$B(x) = \answer {\sage {revenue2}}$

Two UFPD are patrolling the campus on foot. To cover more ground, they split up and begin walking in different directions. Office A is walking at $\sage {officerAspeed3}$ mph while Office B is walking at $\sage {officerBspeed3}$ mph.

Part A. Construct a linear model that describes Officer A’s distance from their starting point, $D$, as a function of minutes, $m$, that have passed.

$D(m) = \answer {\sage {partA3}}$

Part B. Construct a linear model that describes their total distance from each other, $T_1$, as a function of minutes, $m$, that have passed if they were walking in exactly opposite directions (e.g., North/South).

$T_1(m) = \answer {\sage {partB3}}$

Part C. Construct a linear model that describes their total distance from each other, $T_2$, as a function of minutes, $m$, that have passed if they were walking in exactly 90 degrees from each other (e.g., North/East).

$T_2(m) = \answer {\sage {partC3}}$

Exact value needed for the coefficient! DO NOT ROUND.

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A bicyclist is training for a race on a hilly path. Their bike keeps track of their speed at any time, but not the distance traveled. Their speed traveling up a hill is $\sage {speedUp4}$mph, $\sage {speedDown4}$mph when traveling down a hill, and $\sage {speedFlat4}$mph when traveling along a flat portion.

Part A. Construct linear models that describe their distance, $D$ in miles, on a particular portion of the path in terms of the time, $t$ in hours, spent on that part of the path.

$D_{\text {up}}(t) = \answer {\sage {speedUp4*t}}$

$D_{\text {down}}(t) = \answer {\sage {speedDown4*t}}$

$D_{\text {flat}}(t) = \answer {\sage {speedFlat4*t}}$

Part B. Construct linear models that describe their time, $t$ in hours, on a particular portion of the path in terms of the length, $D$ in miles, of that part of the path.

$t_{\text {up}}(D) = \answer {\sage {D/speedUp4}}$

$t_{\text {down}}(D) = \answer {\sage {D/speedDown4}}$

$t_{\text {flat}}(D) = \answer {\sage {D/speedFlat4}}$

Part C. Construct a linear model that describes the total distance of the path, $D$, in terms of the time spent on a particular path if we knew that the time spent on each path was equal.

$D(t) = \answer {\sage {partC4}}$

Part D. Construct a linear model that describes the total time $T$ spent on the path in terms of the distance of a particular part of the path if we knew that all parts of the path are equal length.

$T(D) = \answer {\sage {partD4}}$

Kappa Delta is hosting an all-you-can-eat pancake fundraiser to support the prevention of child abuse. Adult (18+) tickets are $\$ \sage {adultTicketPrice}$ and teen (10-17) tickets are $\$\sage {teenTicketPrice}$. Children under 10 are let in without a ticket. The ticket-sellers only kept track of the total number of tickets sold, $\sage {totalTickets}$, and total revenue, $\$ \sage {totalRevenue}$.

Part A. Construct a linear model that describes the total number of adult tickets, $y$, sold in terms of the number of teen tickets, $x$, sold.

$y = \answer {\sage {eqPartA5}}$

Part B. Construct a linear model that describes the revenue made from selling many adult tickets, $R_a$, in terms of the number of teen tickets, $x$, sold.

$R_a = \answer {\sage {eqPartB5}}$

Part C. Construct a linear model that describes the total revenue made, $R_T$, in terms of the number of teen tickets, $x$, sold.

$R_T = \answer {\sage {eqPartC5}}$

Chemists commonly create a solution by mixing two products of differing concentrations together. For example, a chemist could have large amounts of a $\sage {concA}\%$ acid solution and a $\sage {concB}\%$ acid solution, but need a $\sage {totalVolume}$ liter $\sage {concTotal}$% solution.

Part A. Construct a linear model that describes the volume of the $\sage {concB}\%$ acid solution, $v_{\sage {concB}}$, in terms of the volume of the $\sage {concA}\%$ acid solution, $v$.

$v_{\sage {concB}} = \answer {\sage {eqPartA6}}$

Part B. Construct a linear model that describes the amount of acid in a $\sage {concA}\%$ acid solution, $A_{\sage {concA}}$, in terms of the volume of the $\sage {concA}\%$ acid solution, $v$.

$A_{\sage {concA}} = \answer {\sage {eqPartB6}}$

Part C. Construct a linear model that describes the amount of acid in a $\sage {concB}\%$ acid solution, $A_{\sage {concB}}$, in terms of the volume of the $\sage {concA}\%$ acid solution, $v$.

$A_{\sage {concB}} = \answer {\sage {eqPartC6}}$

Part D. Construct a linear model that describes the amount of acid in a $\sage {concTotal}\%$ acid solution, $A_{\sage {concTotal}}$, in terms of the volume of the $\sage {concA}\%$ acid solution, $v$.

$A_{\sage {concTotal}} = \answer {\sage {eqPartD6}}$