Questions: Question 26 Consider the following linear programming problem: Minimize: 20 X+30 Y Subject to: 2 X+4 Y ≤ 800 6 X+3 Y ≥ 300 X, Y ≥ 0 What is the optimum solution to this problem (X, Y) ? a. (0,0) b. (50,0) c. (0,100) d. (400,0) e. None of these

Question 26 Consider the following linear programming problem: Minimize: 20 X+30 Y Subject to: 2 X+4 Y ≤ 800 6 X+3 Y ≥ 300 X, Y ≥ 0 What is the optimum solution to this problem (X, Y) ? a. (0,0) b. (50,0) c. (0,100) d. (400,0) e. None of these
Transcript text: Question 26 Consider the following linear programming problem: \[ \begin{array}{ll} \text { Minimize: } & 20 X+30 Y \\ \text { Subject to: } & 2 X+4 Y \leq 800 \\ & 6 X+3 Y \geq 300 \\ & X, Y \geq 0 \end{array} \] What is the optimum solution to this problem $(X, Y)$ ? a. $(0,0)$ b. $(50,0)$ c. $(0,100)$ d. $(400,0)$ e. None of these
failed

Solution

failed
failed

Solution Steps

Step 1: Define the Problem

We are tasked with minimizing the objective function \(20X + 30Y\) subject to the constraints:

  1. \(2X + 4Y \leq 800\)
  2. \(6X + 3Y \geq 300\)
  3. \(X, Y \geq 0\)
Step 2: Solve the Linear Programming Problem

By applying the linear programming method, we find the optimal values for \(X\) and \(Y\). The solution yields: \[ X = 50, \quad Y = 0 \]

Final Answer

The optimum solution to the linear programming problem is \(\boxed{(X = 50, Y = 0)}\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Question 1 f(x)=x^3-5x^2+7x-35 exact zeros y-intercept end behavior domain range relative maximum(s) relative minimum(s) Factored form
failedAnswered
Test the claim about the population mean, μ, at the given level of significance using the given sample statistics. Claim: μ=40 ; α=0.09 ; σ=3.09. Sample statistics: x̄=39.6, n=50 Identify the null and alternative hypotheses. Choose the correct answer below. A. H₀: μ<40 Hₐ: μ=40 B. H₀: μ>40 C. H₀: p ≠ 40 Hₐ: μ=40 D. H₀: μ=40 Hₐ: μ ≠ 40 E. H₀: μ=40 F. H₀: μ=40 Hₐ: μ<40 Calculate the standardized test statistic. The standardized test statistic is -0.92. (Round to two decimal places as needed.) Determine the critical value(s). Select the correct choice below and fill in the answer box to complete your choice. (Round to two decimal places as needed.) A. The critical values are ±0.92. B. The critical value is .
failedAnswered
Label each of the following reactions as acid-base, precipitation, or redox Cu(NO3)2(aq) + 2 NaOH(aq) → Cu(OH)2(s) + 2 NaNO3(aq) HCl(aq) + NaOH(aq) → NaCl(aq) + H2O(l) 2 HCl(aq) + Mg(s) → H2(g) + MgCl2(aq) Na2CO3(s) + 2 HNO3(aq) → 2 NaNO3(aq) + H2O(l) + CO2(g) MgBr2(aq) + KOH(aq) → Mg(OH)2(s) + 2 KBr(aq)
failedAnswered
Piano music is typically notated using the staff. Select one: Grand Treble Alto Clef
failedAnswered
A piece of sodium metal is submerged in mineral oil for storage. The sodium displaces 10.7 cubic centimeters of mineral oil. If the density of sodium metal is 0.972 g / cm^3, what is the mass in grams of the submerged piece?