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 $2, and the profit for each model B grate is $1.50. 1000 lb of cast iron and 20 labor- hours are available for the production of grates each day. Because of an excess inventory of model B grates, management has decided to limit the production of model grates to no more than 200 grates per day. (a) If the contribution to the profit of a model A grate is changed to $1.25/grate, what will be the optimal profit? The optimal profit is P = $ 10 X at (x, y) = 20 3 0,5 (b) If the contribution to the profit of a model A grate is changed to $2.25/grate, what will be the optimal profit? 20 The optimal profit is P = $10 x at (x, y) = (0, * ). 3

A company makes pancake mix and cake mix. Each pound of pancake mix uses 0.6 lb of flour and 0.1 lb of shortening. Each pound of cake mix uses 0.4 lb of flour, 0.1 lb of shortening, and 0.4 lb of sugar. Suppliers can deliver at most 6,000 lb of flour, at least 500 lb of shortening, and at most 1,200 lb of sugar. If the profit per pound is $0.45 for pancake mix and $0.35 for cake mix, how many pounds of each mix should be made to earn maximum profit? pancake mix 2000 Xlb lb cake mix 3000 What is the maximum profit (in $)? $3450 X

Frank and his staff make one type of sandal and one type of closed-toe shoe.It takes 3 4 hour to cut the leather for a sandal and 1 2 hour to cut the leather for a shoe. It takes 2 hours to sew the sandal together, and 1 hour to sew the shoe. It takes 2 hours to attach the soles onto a pair of sandals, and 1 hour to attach the soles onto a pair of shoes. A profit of $30 is made on each pair of sandals, and a profit of $40 is  made on each pair of shoes. If the staff is limited to 16 hours for cutting, 24 hours for sewing, and 12 hours for attaching soles, calculate the number of pairs of sandals and shoes they should produce to maximize profit.

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.) ...

type should they produce in a week to maximize their profit? 4 JP Computers produces both laptop and desktop computers. Laptop computers take up 2 cubic feet of space and desktop computers take up 5 cubic feet of space. The maximum capacity on the delivery truck is 800 cubic feet. Due to demand, they need to load at least 300 laptop computers. They profit $225 on each laptop and $280 on each desktop computer. How many of each should they load on the truck to maximize profit?

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charge 8. A wine warehouse expects to sell 30,000 bottles of wine each year. Each bottle costs $9, plus a fixed of $200 per order. If it costs $3 to store a bottle for a year, how many bottles should be ordered at a time and how many orders should the warehouse place in a year to minimize inventory costs?

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…

cost out this recipe. show all work! the recipe: 1 medium head cauliflower, cut up into florets 4 cloves crushed garlic 1/3 cup 1% buttermilk salt and pepper to taste 1 tbsp salted butter, plus optional more for serving the recipe costing info: 1 medium head of cauliflower  $2.99  Garlic $1.57 for 3 heads  Buttermilk $1.75/Quart  Salt $1.39/container  Pepper $1.50/1.5 oz   Butter $3.54/pound

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