A company sells two different products, A & B. The selling price and associated cost information…

A company sells two different products, A & B. The selling price and associated cost information is shown in the table below: Product A Product B Selling price Cost Profit R60 R30 R30 R40 R10 R30 The two products are produced in a common production process and are sold in two different markets. The production process has a capacity of 30 000 labour hours. It takes three hours to produce a unit of product A and one hour to produce a unit of product B. A market survey reveals that the maximum numbers of units of product A that can be sold is 8 000; the maximum for product B is 12 000 units. The products can be sold in any combination. a) Solve the problem graphically to find the optimal product mix. b) What is the shadow price for the constraint on the sales limit for product B? c) How would the solution change if the company wants to minimise production costs with the additional requirement that a minimum of 15 000 labour hours should be used? Question 2 A widget manufacturer makes four models: · An entry level model called the H1 · A regular model called the H2 · A portable model called H3 · A high level model called H4 Each widget requires time to assemble and test. The assembly and testing requirements for each model is shown in the following table (the total time available for these activities for the next production period is also included): H1 H2 H3 H4 Total available Assembly time (hours) Test time (hours) Profit (Rand) 8 2 40 10 2 60 12 4 80 15 5 100 2000 500 As a result of the Covid-19 pandemic there is a shortage of component Z. The supplier has indicated that a total of only 180 components can be supplied for the next production period and of these no more than a 100 can be supplied that are specifically required for models H3 and H4. a) What is the optimal production schedule for the manufacturer? b) Suppose the profit on the entry level model (H1) can be increased to R45. Would this change the optimal production plan? c) Suppose that additional units of component Z can be obtained from another supplier at an additional cost of R2/component for H1 and H2 and R5/component more for H3 and H4. Should any of these be purchased? How many? Question 3 A manufacturer produces a product a three plants and distributes it through four market-service warehouses. The following warehouse and plant information is available: Warehouse Selling price (per unit) Annual demand (units) W1 W2 W3 W4 R1.00 R1.10 R1.00 R0.60 40 000 10 000 20 000 25 000 Plant Production cost (per unit) Annual capacity (units) P1 P2 P3 40 cents 35 cents 45 cents 40 000 30 000 45 000 In addition, the associated transport rates (cents/unit) are available: Plant Warehouse W1 W2 W3 W4 P1 P2 P3 20 20 45 20 10 30 30 35 20 30 40 20 a) Find the optimal production and distribution solution based on cost. b) Find the optimal production and distribution solution based on profit.

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