Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C= 6x+10y subject to 5x+7y>14 8x+6y≥ 16 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y?
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- A sheet of paper 80 cm-by-72 cm is made into an open box (i.e. there's no top), by cutting x-cm squares out of each corner and folding up the sides. Find the value of x that maximizes the volume of the box. Give your answer in the simplified radical form. X = is the max.Which ONE of the following descriptions is CORRECT according to this Normal Form?y = (3 - x)6 + 7 apply the function in economic optimization concept
- Find the optimal solution for the following problem. Maximize C = 4x + 12y subject to 3x + 5y ≤ 12 6x + 2y ≤ 10 and x ≥ 0, y ≥ 0. What is the optimal value of x? What is the optimal value of y? (Round your answer to 3 decimal places.) What is the maximum value of the objective function? (Round your answer to 3 decimal places.)The wage rate of Zeta Corp. employees is 20 million per month, while the cost of one unit of machine is 80 million per month. Currently, Zeta Corp. produces 100 units of output and employs 20 employees and uses 5 units of production machines. This combination of factors of production is the most efficient for the company. So If Zeta Corp. wants to increase its output to 200 units but it cannot change its number of machines (from 5 units), what is the optimal number of employees and production costs of Zeta Corp.?Let say you have 3 products: cake, candy, and bread. The revenue per cake is $8. The revenue per candy is $4. The revenue per bread is $5. Define the number of cake, candy, and bread you are about to produce per day as x, y, and z respectively. The manager wants that the number of cake accounts for at least 30% of the total production per day. What is the correct linear constraint to show this? Group of answer choices 0.3x – 0.7y – 0.7z ≥ 0 0.7x – 0.3y – 0.3z ≥ 0 0.7x – 0.3y – 0.7z ≥ 0 0.3x – 0.7y – 0.3z ≥ 0
- Suppose your total benefit from eating slices of pizza (value in dollars) is 8x−x^2, where x is the number of slices of pizza. Pizza is sold by the slice and costs $2 per slice, and so the total cost of pizza is 2x. Using optimization in levels, what is the optimal amount of pizza for you to eat?The time path of resources is described by X(t) = X(0)e*". If you graphed In X(t) on the y-axis, and had time (t) on the x-axis, then what would be the intercept of the line you drew? In X(0) There isn't enough information to tell gxFor a certain company, the cost for producing x items is 60x + 300 and the revenue for selling x items is 100x – 0.5x². - The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratio polynomial.) Part b: Find two values of x that will create a profit of $300. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x – 1). The order of the list does not matter. To enter va, type sqrt(a). x = Part c: Is it possible for the company to make a profit of $15,000?