Use the following problem statement to answer questions $17-18.$

A company produces regular and premium gasoline for independent service stations. The company manufactures the products by blending three components: $1,2,$ and $3.$ The gasolines are sold at different prices while the petroleum components have different costs. Data show that regular gasoline can be sold for $$2\mathrm{.}90$ per gallon and premium gasoline for $$3\mathrm{.}00$ per gallon. For the current production period, the company can obtain the three components at the cost per gallon and in the quantities shown in Table $1.$ Table $2$ shows the product specifications that restrict the amount of each component used in each product. Current commitments to distributors require the company to produce at least $10,000$ gallons of regular gasoline. The company wants to determine how to mix the three components into the two gasoline products and maximize total profit. Formulate a model to determine how many gallons of each component should be used in the regular gasoline and the premium gasoline. $[$Note: Xij $=$ no$.$ of gallons of component i used in gasoline j$,$ where i $=1,2,3$ and j $=$ R $($Regular$)$ and P $($Premium$).]$

Table $1$

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Component Cost$/$gallon Maximum Available

$1$: $$2\mathrm{.}5013,000$ gallons

$2$: $$2\mathrm{.}6012,000$ gallons

$3$: $$2\mathrm{.}8415,000$ gallons

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Table $2$

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Product Specifications

Regular gas: At least $31\%$ component $1$

Regular gas: At most $24\%$ component $2$

Premium gas: At least $35\%$ component $2$

Premium gas: At most $40\%$ component $3$

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Flag question: Question $17$

Question $176$ pts

Which of the following constraints is correct?

Group of answer choices

X$2$R $=0\mathrm{.}35($X$3$P $+$ X$3$P $+$ X$3$P$)$

X$2$R $>=0\mathrm{.}31($X$2$R $+$ X$2$P $+$ X$2$R$)$

X$3$R $=0\mathrm{.}40($X$1$R $+$ X$2$R $+$ X$3$P$)$

X$2$P $>=0\mathrm{.}35($X$1$P $+$ X$2$P $+$ X$3$P$)$

Flag question: Question $18$

Question $186$ pts

Which of the following constraints is correct?

Group of answer choices

X$2$R $+$ X$1$P $<=12,000$

X$3$R $+$ X$2$R $<=15,000$

X$1$R $+$ X$1$P $<=13,000$

X$1$P $+$ X$3$P $>=15,000$