Kane Manufacturing has a division that produces two models of fireplace grates, x units of model A and y units of model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $3.50, and the profit for each model B grate is $1.50. Also, 1000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day. Because of a backlog of orders for model A grates, Kane's manager had decided to produce at least 150 of these grates a day. Operating under this additional constraint, how many grates of each model should Kane produce to maximize profit? (x, y)  =

A bakery sells pies and cakes. Each pie costs $2 to produce, requires a half an hour of labor, and sells for $3; while each cake costs $3, requires an hour of labor, and sells for $5. How many pies and cakes, respectively, should be produced in each 8 hour day if the bakery spends no more than $30 per day on supplies?

It takes 12 units of carbohydrates and 6 units of protein to satisfy Jacob's minimum weekly requirements. The meat contains 2 units of carbohydrates and 2 units of protein per pound. The cheese contains 3 units of carbohydrates and 1 unit of protein per pound. The meat costs $3.40 per pound and the cheese costs $4.50 per pound. How many pounds of each are needed to fulfill the minimum requirements at minimum cost? What is Jacob's minimum cost? He should buy pound(s) of meat and pound(s) of cheese. (Round your answer to the nearest tenth.) The minimum cost is $. (Round to the nearest cent as needed.) ...

Question 4 Maggie works at a very popular freshly squeezed lemonade stand on a beach that sells regular lemonade and strawberry lemonade. To make a glass of regular lemonade it takes 4 whole lemons. To make a glass of strawberry lemonade it takes 3 whole lemons and 2 average sized strawberries. The owners figured they have a budget so that each morning a truck delivers 900 lemons to the stand and 408 strawberries to the stand. On each glass of regular lemonade, a profit of R1,95 is made. The stand is able to charge more for strawberry lemonades and a profit of R2,10 is made on each glass of that. The owners want Maggie to sell at least twice the amount of strawberry lemonade each day as regular lemonade because more profit is made on the strawberry lemonade. They have also asked that at least 50 strawberry lemonades get sold each day because the strawberries spoil more quickly than the lemons. How many regular lemonades and how many strawberry lemonades should Maggie sell each day to…

A toy factory creates miniature steel train engines and box cars. The fabrication department has 3,679 minutes available per week and the assembly and finishing department has 3,099 minutes available per week. Manufacturing one miniature steel train engine requires 8 minutes of fabrication and 5 minutes of assembling and finishing. Manufacturing one miniature steel box car requires 4 minutes of fabrication and 5 minutes of assembling and finishing. The profit on each miniature steel train engine is $8.00 and the profit on each miniature steel box car is $7.25. How many steel train engines and steel box cars should be produced each week to obtain the maximum profit? Find the maximum weekly profit. (Use x for box car and y for train engine.) Maximize P subject to %3D < 3, 679 < 3, 099 Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes below. If more than one solution exists, enter only one of the multiple solutions below. If needed round toys…

Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $1.75, and the profit for each model B grate is $1.25. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day. Maximize      P = 1.75x + 1.25y subject to   3x  +  4y  ≤ 1000      Resource 1   6x  +  3y  ≤ 1200   Resource 2       x  ≤ 180   Resource 3       y  ≥ 0         x  ≥ 0   (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)$ (b) Identify the binding and nonbinding constraints. constraint 1          constraint 2       constraint 3

Kane Manufacturing has a division that produces two models of grates, model A and model B. To produce each model A grate requires 3 pounds of cast iron and 6 minutes of labor. To produce each model B grate requires 4 pounds of cast iron and 3 minutes of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $1.50. Available for grate production each day are 1000 pounds of cast iron and 20 labor-hours. Because of an excess inventory of model A grates, management has decided to limit the production of model A grates to no more than 180 grates per day. Maximize      P = 2x + 1.5y subject to   3x  +  4y  ≤ 1000      Resource 1   6x  +  3y  ≤ 1200   Resource 2       x  ≤ 180   Resource 3       y  ≥ 0         x  ≥ 0   (a) Find the shadow price for Resource 2. (Round your answer to the nearest cent.)$  (b) Identify the binding and nonbinding constraints. constraint 1           constraint 2        constraint 3

A company produces widgets at plants 1 and 2. It costs 125x1y2 dollars to produce x units at plant 1 and 235x1y3 dollars to produce x units at plant 2.Each plant can produce up to 500 units. Each unit produced can be sold for $10. At most 800 widgets can be sold. Determine how -the company canmaximize its profit.

A company makes three components for sale. The components are processed on two machines: a shaper and a grinder. The time required. (in minutes) on each machine are as follows: Component Shaper Time Grinder Time A 6 4 B 4 5 C 4 2 The shaper is available for 7200 min. and grinder for 6600 min. No more than 200 units of component C can be sold, but up to 1000 units of each of the other components can be sold. In fact the company has orders for 600 units of component A that must be satisfied. The profit contributions for components A, B and C are $8, $6 and $9 respectively. Formulate the problem for deciding the production quantities. Solve the problem using Excel Solver. Run the sensitivity analysis report in Excel Solver. What are the objective coefficient ranges (Range of Optimality) for each coefficient. Interpret these. What are the dual prices for each constraint? Interpret these. What are the right-hand side ranges (Range of Feasibility)? Interpret them. If more time is…

an artist makes three types of ceramic statues( large, medium and small) at monthly cost of $880 for 250 statues. the manufacturing costs for the three types are $5,$4,$3. if the statues sell for $26, $18, and $15, respectively, how many of each type should be made to produce $4,240 in monthly revenue Large ? Medium ? Small ?