Question 2 Nova Lighting Company manufactures four families of household lighting at its factory. The product families are table lamps, floor lamps, ceiling fixtures, and pendant lamps. Table 1 shows the average material costs for each of the products. Table 1: Average material costs Product Material Unit Cost (8) Table (t) Floor (f) 66 85 Ceiling (c) 50 Pendant (p) 8 0 Each product is made in one of two production departments by purchasing components, assembling and testing the product, and finally packaging it for shipping. Table lamps and floor lamps go through the assembly and packaging in Department 1, while ceiling fixtures and pendant lamps go through the process in Department 2. Variable production costs and capacities (measured in units of product) are shown in Table 2. Table 2: Production costs and Capacities Process Department 1 Department 2 Department Regular Time Unit Cost (8) Capacity 100,000 90,000 lot Overtime Unit Cost (8) Capacity 18 18 25,000 24,000 3 Average selling prices for the four products are known and estimates have been made for the market demand for each product at these prices. These figures are shown in Table 3, Table 3: Demands and prices Table (t) Floor (f) Ceiling (c) 100 Pendant (p) 160 120 Selling price (S/unit) Potential sales ('000) 60 100 35 Accordingly, we define the following decision variables: X : units of product type i produced during regular time (i = tf.cp). Y; : units of product type produced during overtime G = tf.cp). Using ONLY the decision variables defined above, write the LINEAR expression(s) for each of the items below: a. (5 pts. The company's objective is to maximize their profit. Write down separate expressions for the Revenue and the Costs (Materials and Production) Marimite b. (4 pts.) Capacities at Department I should not be exceeded. CoB 291 - Mock Test 1. Page 4 of 5 c. (4 pts.) Production of table lamps and ceiling fixtures should cover the corresponding potential sales. Sales levels can also be affected by advertising expenditures. Starting with the demand levels in Table 3, an increase of up to $10,000 in advertising raises the demand by the percentage shown in Table 4 below. Table 4: Advertising expenditure effect Product Advertising effect Table (t) 12% Floor (1) 10% Ceiling (c) 8% Pendant (P) 15% An expenditure of less than $10,000 in advertising will lead to a proportional effect on demand. For example, an increase in advertising of $5,000 for table lamps would raise demand by 6%, or 3,600 units. Accounting for this we need to define the following new decision variables: M : Amount of money spent on advertising product type iit,f.cp). Using ALL the decision variables defined so far, answer the following questions: d. (4 pts.) Would the objective function defined in (a) require modifications (Y/N)? If so, state them below. e. (5 pts) How would the constraint for covering sales of table lamps be modified? State the modified constraint below. e. (5 pts) How would the constraint for covering sales of table lamps be modified? State the modified constraint below. f. (3 pts. There is a budget limit of $18,000 on the total amount to be spent on advertising among all four products. Write a linear expression to model this requirement. Question 2 Nova Lighting Company manufactures four families of household lighting at its factory. The product families are table lamps, floor lamps, ceiling fixtures, and pendant lamps. Table 1 shows the average material costs for each of the products. Table 1: Average material costs Product Material Unit Cost (8) Table (t) Floor (f) 66 85 Ceiling (c) 50 Pendant (p) 8 0 Each product is made in one of two production departments by purchasing components, assembling and testing the product, and finally packaging it for shipping. Table lamps and floor lamps go through the assembly and packaging in Department 1, while ceiling fixtures and pendant lamps go through the process in Department 2. Variable production costs and capacities (measured in units of product) are shown in Table 2. Table 2: Production costs and Capacities Process Department 1 Department 2 Department Regular Time Unit Cost (8) Capacity 100,000 90,000 lot Overtime Unit Cost (8) Capacity 18 18 25,000 24,000 3 Average selling prices for the four products are known and estimates have been made for the market demand for each product at these prices. These figures are shown in Table 3, Table 3: Demands and prices Table (t) Floor (f) Ceiling (c) 100 Pendant (p) 160 120 Selling price (S/unit) Potential sales ('000) 60 100 35 Accordingly, we define the following decision variables: X : units of product type i produced during regular time (i = tf.cp). Y; : units of product type produced during overtime G = tf.cp). Using ONLY the decision variables defined above, write the LINEAR expression(s) for each of the items below: a. (5 pts. The company's objective is to maximize their profit. Write down separate expressions for the Revenue and the Costs (Materials and Production) Marimite b. (4 pts.) Capacities at Department I should not be exceeded. CoB 291 - Mock Test 1. Page 4 of 5 c. (4 pts.) Production of table lamps and ceiling fixtures should cover the corresponding potential sales. Sales levels can also be affected by advertising expenditures. Starting with the demand levels in Table 3, an increase of up to $10,000 in advertising raises the demand by the percentage shown in Table 4 below. Table 4: Advertising expenditure effect Product Advertising effect Table (t) 12% Floor (1) 10% Ceiling (c) 8% Pendant (P) 15% An expenditure of less than $10,000 in advertising will lead to a proportional effect on demand. For example, an increase in advertising of $5,000 for table lamps would raise demand by 6%, or 3,600 units. Accounting for this we need to define the following new decision variables: M : Amount of money spent on advertising product type iit,f.cp). Using ALL the decision variables defined so far, answer the following questions: d. (4 pts.) Would the objective function defined in (a) require modifications (Y/N)? If so, state them below. e. (5 pts) How would the constraint for covering sales of table lamps be modified? State the modified constraint below. e. (5 pts) How would the constraint for covering sales of table lamps be modified? State the modified constraint below. f. (3 pts. There is a budget limit of $18,000 on the total amount to be spent on advertising among all four products. Write a linear expression to model this requirement