Suppose there are two factories with the following total cost functions TC1 =q1 and TC,= q!/2 respectively. For orders strictly greater than 1 unit, the firm should not use factory 2 at all the firm should produce no more than 1 unit in factory 2 the firm should not use factory 1 at all the firm should produce no more than 1 unit in factory 1
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- A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $5/unit of Product A and a profit of $7/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit?A campaign to promote a brand of dairy products is based on the free distribution of yogurts with lemon or strawberry flavor. It is decided to distribute at least 30,000 yogurts. Every lemon yogurt needs for its elaboration 0.5 gr. of a fermentation product and each strawberry yogurt needs 0.2 gr. of that same product. It has 9 kgs. of that product for fermentation. The cost of producing a yogurt of strawberry is twice that of a lemon yogurt. How many yogurts of each type must be produced so that the cost of the campaign is minimal?.A firm has 2 plants with different functions: - Plant 1: MC = 30 + Q - Plant 2: MC = 20 + 2Q How to allocation output between the 2 plants to minimize total cost of producing 50 units of output? What is the minimum total cost?
- Suppose shop A sells q chocolates for q^2+2q dollars whereas the price per chocolate in shop B is 10 dollars. We say that we ''profit from shop A" if we purchase the same quatity of chocolates from shop A at a relatively cheaper price as compared to shop B. Otherwise, we say that we are at a loss. 1.Prove that we will get a large number of chocolates for a cheaper price in shop B compared to shop A. 2.What is the maximum number of choclates we can purchase from shop A so that we do not lose any money. 3.How many chocolates should we buy from shop A to maximise our profit (compared to shop B)? Thank you so much!With fixed costs of Ksh. 400,000, a firm has average total costs of Ksh. 3,000 and average variable costs of Ksh. 2,500. Its output is?Suppose that a company has received an order for 200 units of its product and wishes to distribute its production between two of its plants, Plant 1 and Plant 2. Let x and y be the outputs of plants 1 and 2, respectively, and suppose that the function of total cost is given by c = f(x,y) = 2x2 + xy + y2 + 200 How should production be distributed to minimize costs? What would you do if now instead of 1 restriction, you had 2 restrictions?
- Suppose that a manufacturer produces two brands of a product, brand 1 and brand 2. Suppose the demand for brand 1 is x = 85 − p1 thousand units and the demand for brand 2 is y = 95 − p2 thousand units, where p1 and p2 are prices in dollars. If the joint cost function is C = xy, in thousands of dollars, how many of each brand should be produced to maximize profit?Niue Vanilla has had two successive years in which the Vanilla bean harvest has stretched the firm’s capacity within their drying sheds. Pita, the manger for the drying operation must now make a decision on capacity for next year. Estimated profits under each of the three possible states of nature are as shown in the table below, along with 3 possible alternatives he is considering: Do Nothing, Expand the Drying Shed operation, or Subcontract to a local farmer group who can do some of the drying. Which alternative should be selected if the decision criterion is: Maximax? Maximin?A firm manufactures two types of shafts A and B. For any month it must produce 250 shafts A and 100 shafts B. The maximum total requirement of shafts A and B is 1,250 and minimum total requirement is 500. Both shafts are to be processed on machines M1 and M2. Total number of machines M1 and M2 available are 15 each. Processing times in hours for each shaft on machines M1 and M2 are as follows: A B M1 1.5 2 M2 1 1.5 Profit/unit (K) 400 600 If the firm has 25 working days a month, each of 8 hours, Formulate the linear programming model for the problem. Solve the problem by graphical method.
- A company has found that the marginal cost (in thousands of dollars) to produce x central air conditioning units is C′(x)=30x3x2+e, where x is the number of units produced. (a) Find the cost function, given that the company incurs a fixed cost of $13,000 even if no units are built. (b) The company will seek a new source of investment income if the cost is more than $18,000 to produce 5 units. Should they seek this new source?A diesel engine uses type A filter and high-grade lubricating oil costing P55 per liter. With this filter, the oil and the filter have to be changed every 500hrs. of operation, and 5L of oil have to be added every 100hrs. This filter costs P1480 a piece. Eighty liters of oil fill the engine. Another type, filter B, costing of P1200 may be used with a lower grade of oil costing P48 per liter. However, if this filter is used, the oil and filter have to be changed every 300hrs and 10 liters are added after each 150hrs the engine is used. Hint: Consider the cost per hour.A company is involved in the production of two items (X and Y). The resources need to produce X and Y are twofold, namely machine time for automatic processing and craftsman time for hand finishing. The table below gives the number of minutes required for each item: Machine time Craftsman time Item X 13 20 Item Y 19 29 The company has 40 hours of machine time available in the next working week but only 35 hours of craftsman time. Machine time is costed at £10 per hour worked and craftsman time is costed at £2 per hour worked. Both machine and craftsman idle times incur no costs. The revenue received for each item produced (all production is sold) is £20 for X and £30 for Y. The company has a specific contract to produce 10 items of X per week for a particular customer. Formulate the problem of deciding how much to produce per week as…