Sarah makes bracelets and necklaces to sell at a craft store. Each bracelet makes a profit of $7, takes 1 hour to assemble, and costs $2 for materials. Each necklace makes a profit of $12, takes 2 hour to assemble, and costs $3 for materials. Sarah has 48 hours available to assemble bracelets and necklaces. (𝑥=number of bracelets, 𝑦=number of necklaces).Maximize 𝑍=12𝑥+7𝑦Constraints: 𝑥≥0,𝑦≥0 2𝑥+3𝑦≤78 𝑥+2𝑦≤48 22. How much optimum profit did she realize?Group of answer choicesP 468P 270P 300P 168
Question
Sarah makes bracelets and necklaces to sell at a craft store. Each bracelet makes a profit of 2 for materials. Each necklace makes a profit of 3 for materials. Sarah has 48 hours available to assemble bracelets and necklaces. (𝑥=number of bracelets, 𝑦=number of necklaces).Maximize 𝑍=12𝑥+7𝑦Constraints: 𝑥≥0,𝑦≥0 2𝑥+3𝑦≤78 𝑥+2𝑦≤48 22. How much optimum profit did she realize?Group of answer choicesP 468P 270P 300P 168
Solution
The problem is a linear programming problem. We are asked to maximize the profit function Z = 12x + 7y subject to the constraints x ≥ 0, y ≥ 0, 2x + 3y ≤ 78, and x + 2y ≤ 48.
First, we need to find the feasible region by graphing the constraints. The feasible region is the set of all points that satisfy all the constraints.
Next, we find the vertices of the feasible region. These are the points where the boundary lines of the constraints intersect.
Then, we evaluate the profit function Z at each of the vertices. The maximum value of Z is the maximum profit.
The vertices of the feasible region are (0,0), (0,24), (18,15), and (39,0).
Evaluating Z at these points gives:
Z(0,0) = 12(0) + 7(0) = 0 Z(0,24) = 12(0) + 7(24) = 168 Z(18,15) = 12(18) + 7(15) = 216 + 105 = 321 Z(39,0) = 12(39) + 7(0) = 468
So, the maximum profit is P 468.
Similar Questions
Marisol is making bracelets and rings to sell at a craft fair. She plans to sell each bracelet for $6 and each ring for $8. The craft fair committee charges a $25 fee to sell at the fair, and it costs Marisol $2 to make a bracelet and $4 to make a ring. If Marisol wants to sell at least $600 in jewelry and spend less than $300 for supplies and the fee, which system of inequalities represents the situation? Let b represent the number of bracelets and r represent the number of rings.
A company is preparing to make gold jewellery during a 2-month period for the Christmas season. It can make bracelets, necklaces, and pins. Each bracelet requires 6.3 ounces of gold and 17 hours of labour, each necklace requires 3.9 ounces of gold and 10 hours of labour, and each pin requires 3.1 ounces of gold and 7 hours of labour. The company has available 125 ounces of gold and 320 hours of labour. A bracelet sells for $1,650, a necklace for $850, and a pin for $790. If the company is aiming to maximize profit, what is the maximum profit it can achieve from making bracelets, necklaces, and pins using the resources currently at its disposal? A. Objective value Z = 32460.47 B. Objective value Z = 32463.47 C. Objective value Z = 32461.47 D. Objective value Z = 32746.47
A business owner makes 50 items by hand in 40 hours. She could have earned $20 an hour working for someone else. Her total explicit costs are $200. If each item she makes sells for $15, her economic profit equals:
Mrs Chan will make a profit which is 12% of the original price, if she sells the necklace at $4256. What will be her profit if she sells the necklace at $4340?
opportunity cost of making a necklace
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.