A pizza shop is selling three different types of pizzas (P1, P2, P3). Each of these pizzas uses three major types of ingredients with different proportions as shown in Table 1. Assume the costs (£) of the raw ingredients A, B and C are a, b, and c respectively. a. Construct a matrix equation for the costs of three pizzas in terms of the costs of the raw ingredients. b. The pizza shop is opened for 3 days a week. 10P1, 6P2, and 7P3 pizzas were sold on Day1. On Day 2, 15P1, 11P2 and 9P3 pizzas were sold. On Day 3, 9P1, 13P2, and 10P3 pizzas were sold. Construct a matrix equation for the total cost of making pizzas for each of the three days in terms of the costs of the raw ingredients. c. The total costs of making pizzas on Day 1, Day 2 and Day 3 were £250, £380 and £340 respectively. By using the above constructed matrices, calculate the cost of each ingredient using Cramer’s rule.
A pizza shop is selling three different types of pizzas (P1, P2, P3). Each of these pizzas uses three major types of ingredients with different proportions as shown in Table 1. Assume the costs (£) of the raw ingredients A, B and C are a, b, and c respectively.
a. Construct a matrix equation for the costs of three pizzas in terms of the costs of the raw ingredients.
b. The pizza shop is opened for 3 days a week. 10P1, 6P2, and 7P3 pizzas were sold on Day1. On Day 2, 15P1, 11P2 and 9P3 pizzas were sold. On Day 3, 9P1, 13P2, and 10P3 pizzas were sold. Construct a matrix equation for the total cost of making pizzas for each of the three days in terms of the costs of the raw ingredients.
c. The total costs of making pizzas on Day 1, Day 2 and Day 3 were £250, £380 and £340 respectively. By using the above constructed matrices, calculate the cost of each ingredient using Cramer’s rule.
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