The Following Linear Programming Problem Has Been Written to Plan

question 47

Multiple Choice

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits. X₁ = number of product 1 produced in each batch
X₂ = number of product 2 produced in each batch
$$\begin{array} { l l } \text { MAX: } & 150 X _ { 1 } + 250 X _ { 2 } \\\text { Subject to: } & 2 X _ { 1 } + 5 X _ { 2 } \leq 200 \\& 3 X _ { 1 } + 7 X _ { 2 } \leq 175 \\& X _ { 1 } , X _ { 2 } \geq 0\end{array}$$ How much profit is earned if the company produces 10 units of product 1 and 5 units of product 2?

• A) 750
• B) 2500
• C) 2750
• D) 3250

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Definitions:

Explosive Reactions

Chemical reactions that occur with a sudden release of energy, often accompanied by the production of heat and light.

Nitro Groups

Functional groups in organic chemistry consisting of one nitrogen atom connected by a double bond to one oxygen atom and by a single bond to another oxygen atom; they are denoted as NO2 and contribute to the reactivity of molecules.

Neutral Oxygen Balance

A term in explosives chemistry indicating that an explosive compound has an oxygen balance of zero, meaning it has exactly enough oxygen to oxidize all its components.

Oxidize

A chemical process involving the transfer of electrons from a substance to an oxidizing agent, increasing the oxidation state of the substance.